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emen4

Total questions: 128

Worksheet time: 1hrs 14mins

Name
Class
Date
1.

What is the role of the nautical almanac in celestial navigation?

a)

To provide positions of celestial bodies at various times

b)

To measure the angle between celestial bodies

c)

To calculate magnetic variation

d)

To determine the height of the observer

2.

Accurate timing is not necessary when performing celestial navigation computations.

(a)  

3.

What is the purpose of plotting lines of position (LOPs) in celestial navigation?

a)

To determine the ship's location by intersecting LOPs from different celestial observations

b)

To adjust for magnetic variations in navigation

c)

To simplify the corrections applied to observed altitudes

d)

To identify the nearest landmass

4.

When the natural horizon is not visible, navigators use an (a)   horizon.

5.

How does vessel movement affect celestial observations?

a)

It introduces difficulty in maintaining a steady view through the sextant.

b)

It alters the geographical position of the celestial body.

c)

It changes the refraction correction required.

d)

It makes the horizon invisible.

6.

A chronometer is used in celestial navigation to record the (a)   of the observation.

7.

When is the best time to observe stars for celestial navigation?

a)

At twilight

b)

At noon

c)

During a full moon

d)

At midday

8.

Magnetic variations directly affect the observed altitude of celestial bodies.

(a)  

9.

A nautical almanac provides the positions of celestial bodies at various times throughout the (a)   .

10.

The primary tool used in celestial navigation to measure the angle between a celestial body and the horizon is the (a)   .

11.

A nautical almanac provides the positions of celestial bodies at various times throughout the year.

(a)  

12.

When observing the Sun at noon, what characteristic of the Sun's position simplifies celestial navigation calculations?

a)

The Sun is at its highest point in the sky (zenith).

b)

The Sun is directly aligned with the magnetic north.

c)

The Sun is least affected by atmospheric refraction.

d)

The Sun's altitude equals the observer's latitude.

13.

Why is accurate timing crucial in celestial navigation?

a)

To correlate observations with celestial data in the almanac

b)

To determine the exact position of the sextant

c)

To adjust for magnetic variations

d)

To ensure the sextant reading is error-free

14.

Index error is a systematic error in the sextant that must be corrected before computing the true altitude.

(a)  

15.

The process of determining the ship’s position by using the predictable movements of celestial bodies, measuring their altitude with a sextant, and applying corrections to compute true altitude is called _____.

4 lines
16.

How does the height of the observer above sea level affect celestial navigation?

a)

It changes the dip correction applied to the observed altitude.

b)

It affects the index error of the sextant.

c)

It determines the choice of celestial body for observation.

d)

It has no effect on the navigation process.

17.

What is the purpose of a chronometer in celestial navigation?

a)

To record the precise time of a celestial observation

b)

To measure the altitude of celestial bodies

c)

To calibrate the sextant

d)

To correct for magnetic variations

18.

The sextant is used to measure the distance between two celestial bodies.

(a)  

19.

What is the azimuth in celestial navigation?

a)

The bearing from the observer to the geographical position of the celestial body

b)

The altitude of a celestial body as observed through a sextant

c)

The angle between the horizon and the celestial body

d)

The corrected altitude after applying all necessary corrections

20.

Magnetic variation must be considered to align celestial navigation readings with (a)   .

21.

What is the role of the nautical almanac in celestial navigation?

a)

It provides the positions of celestial bodies at various times throughout the year.

b)

It lists all known nautical hazards.

c)

It describes the construction of navigation instruments.

d)

It provides instructions for using a sextant.

22.

What is the role of a sextant in celestial navigation?

a)

To measure the angle between a celestial body and the horizon

b)

To calculate the ship's position directly

c)

To adjust for the Earth's curvature

d)

To determine the time of day

23.

To correct for the observer's height above sea level, navigators apply the (a)   correction.

24.

When observing stars, twilight is the most suitable time to take measurements.

(a)  

25.

In celestial navigation, why are the Sun and Moon commonly used as celestial bodies for observation?

a)

They are easily visible and their positions are well-documented in nautical almanacs.

b)

They do not require a sextant for observation.

c)

Their true altitude does not require correction.

d)

Their movement is easier to predict than that of stars.

26.

The (a)   is an error in the sextant that must be identified and corrected to ensure accurate altitude computation.

27.

Refraction correction is added to the observed altitude to calculate the true altitude.

(a)  

28.

What is the primary advantage of celestial navigation over GPS?

a)

It is faster to use.

b)

It is independent of external systems like satellites or radio signals.

c)

It requires less training.

d)

It provides more accurate results.

29.

What does the refraction correction adjust for?

a)

The bending of light in the atmosphere

b)

The observer's height above sea level

c)

The alignment of the sextant's mirrors

d)

The difference between magnetic and true north

30.

What is the significance of the geographical position (GP) of a celestial body?

a)

It represents the point on the Earth's surface directly beneath the celestial body.

b)

It indicates the altitude of the celestial body.

c)

It corresponds to the observer's position on Earth.

d)

It is the reference point for magnetic variation corrections.

31.

Celestial navigation relies on the predictable movements of celestial bodies to determine a ship's position.

(a)  

32.

What does the term 'true altitude' mean in the context of celestial navigation?

a)

The corrected altitude of a celestial body as it would appear from the Earth's center

b)

The altitude of a celestial body above the horizon as observed through a sextant

c)

The altitude corrected for the observer's height only

d)

The apparent altitude of a celestial body during twilight

33.

Which celestial body is commonly observed at twilight for navigation purposes?

a)

Stars

b)

The Sun

c)

The Moon

d)

Planets

34.

What is the artificial horizon used for in celestial navigation?

a)

To provide a reference plane when the natural horizon is not visible

b)

To measure the altitude of stars directly

c)

To adjust the sextant for index error

d)

To determine the ship's speed

35.

The dip correction increases with the observer's height above sea level.

(a)  

36.

What is the purpose of a chronometer in celestial navigation?

a)

To record the precise time of an observation

b)

To measure the angle of celestial bodies

c)

To calculate corrections for altitude measurements

d)

To determine the observer's location on a chart

37.

Which tool is essential for measuring the angle between a celestial body and the horizon?

a)

Sextant

b)

Chronometer

c)

Artificial horizon

d)

Nautical almanac

38.

Twilight is often the most suitable time to observe (a)   for navigation purposes.

39.

Why is it important to apply a dip correction to the observed altitude?

a)

To account for the observer's height above sea level

b)

To correct for atmospheric refraction

c)

To adjust for the Earth's curvature

d)

To eliminate instrument errors

40.

Which correction accounts for the observer's height above sea level?

a)

Dip correction

b)

Index error correction

c)

Refraction correction

d)

Parallax correction

41.

The bending of light as it passes through the Earth's atmosphere, which affects the apparent altitude of celestial bodies, is known as (a)   .

42.

What is the purpose of taking multiple observations and averaging in celestial navigation?

a)

To reduce observational inaccuracies caused by vessel movement or environmental factors

b)

To ensure the observed altitude matches the true altitude

c)

To simplify the computation process

d)

To avoid recording incorrect times

43.

Which type of error in the sextant must be corrected to ensure accurate altitude readings?

a)

Index error

b)

Parallax error

c)

Magnetic variation

d)

Time error

44.

Which of the following tools is NOT used in celestial navigation?

a)

A sextant

b)

A barometer

c)

A nautical almanac

d)

A chronometer

45.

What is the purpose of the index arm on a sextant?

a)

To align the image of the celestial body with the horizon

b)

To measure the altitude of the observer

c)

To stabilize the sextant against vessel motion

d)

To provide light for observations

46.

How is the true altitude of a celestial body calculated?

a)

By correcting the observed altitude for index error, dip, and refraction

b)

By measuring the angle with a sextant directly

c)

By calculating the distance to the celestial body

d)

By using the Nautical Almanac's data without corrections

47.

Which correction is necessary to adjust for the bending of light through the Earth's atmosphere?

a)

Refraction correction

b)

Index error correction

c)

Dip correction

d)

Parallax correction

48.

What is the function of an artificial horizon in celestial navigation?

a)

To provide a reference when the natural horizon is obscured

b)

To enhance the visibility of celestial bodies

c)

To measure time accurately

d)

To calculate magnetic variation

49.

The artificial horizon is used when the natural horizon is not visible, such as during bad weather.

(a)  

50.

What is the primary purpose of celestial navigation?

a)

To determine a ship's position using observations of celestial bodies

b)

To track the movement

51.

What is the primary purpose of celestial navigation?

a)

To determine a ship's position using observations of celestial bodies

b)

To track the movement of stars across the sky

c)

To calculate time zones based on longitude

d)

To predict weather patterns

52.

What information is required to locate an entry in the sight reduction tables?

a)

The local hour angle (LHA), the declination of the celestial body, and the latitude of the assumed position

b)

The observed altitude (Ho), the azimuth (Zn), and the assumed position

c)

The magnetic variation, the compass deviation, and the bearing

d)

The time of observation, the altitude of the celestial body, and the observer's position

53.

What is the primary purpose of celestial navigation?

a)

To determine the observer's position at sea by observing celestial bodies

b)

To calculate the angular distance between celestial bodies

c)

To measure the time of day using the sun

d)

To correct magnetic compass errors

54.

Which correction is applied to account for atmospheric bending of light?

a)

Refraction correction

b)

Parallax correction

c)

Index error correction

d)

Dip correction

55.

Which of the following is NOT a component of the PZX triangle in celestial navigation?

a)

The Celestial Pole (P).

b)

The Zenith (Z).

c)

The Celestial Body (X).

d)

The Equator.

56.

What is the formula for calculating the intercept (a) in celestial navigation?

a)

a = Ho - Ha

b)

a = Ha - Ho

c)

a = Ho + Ha

d)

a = Ha + Ho

57.

What correction accounts for the observer's height above sea level?

a)

Dip correction

b)

Index error correction

c)

Parallax correction

d)

Refraction correction

58.

The observed altitude (Ho) is corrected for various factors, including (a)   and parallax, to ensure accuracy.

59.

What are the key components of the PZX triangle in celestial navigation?

a)

The celestial pole (P), the observer's zenith (Z), and the celestial body (X)

b)

The celestial equator, the observer's zenith, and the horizon

c)

The celestial horizon, the Earth's center, and the observer's position

d)

The ecliptic, the equator, and the prime meridian

60.

What is the intercept (a) in celestial navigation?

a)

The difference between the observed altitude (Ho) and the calculated altitude (Ha).

b)

The sum of the observed altitude (Ho) and the calculated altitude (Ha).

c)

The product of the observed altitude (Ho) and the calculated altitude (Ha).

d)

The ratio of the observed altitude (Ho) to the calculated altitude (Ha).

61.

What is a practical step navigators take to minimize errors in celestial navigation?

a)

Double-check all readings and calculations

b)

Use a digital sextant

c)

Avoid observations during cloudy weather

d)

Only observe the sun and the moon

62.

What is the significance of the declination (Dec) of a celestial body?

a)

It represents the celestial body's angular distance north or south of the celestial equator

b)

It indicates the celestial body's altitude above the horizon

c)

It is used to correct the observed altitude (Ho)

d)

It determines the azimuth (Zn) of the celestial body

63.

What does the intercept (a) represent in celestial navigation?

a)

It is the observed altitude (Ho) directly.

b)

It is the calculated altitude (Ha) directly.

c)

It is the difference between the observed altitude (Ho) and the calculated altitude (Ha).

d)

It is the angle of the celestial body relative to the horizon.

64.

What does the intercept (a) in celestial navigation represent?

a)

The difference between the observed altitude (Ho) and the calculated altitude (Ha).

b)

The sum of the observed altitude (Ho) and the calculated altitude (Ha).

c)

The distance between the observer and the celestial body.

d)

The angle of declination of the celestial body.

65.

What relationship does the spherical law of cosines provide in the PZX triangle?

a)

It relates the observer's latitude, the celestial body's declination, and the hour angle to the calculated altitude (Ha)

b)

It relates the angular distances between the celestial pole, zenith, and celestial body

c)

It provides the azimuth (Zn) of the celestial body

d)

It calculates the dip of the horizon

66.

What does a negative intercept (a) indicate?

a)

The observer is farther from the celestial body than the assumed position

b)

The observer is closer to the celestial body than the assumed position

c)

The observer is directly under the celestial body

d)

The observed altitude (Ho) equals the calculated altitude (Ha)

67.

If the intercept (a) is negative, what does this indicate about the observer's position?

a)

The observed position is farther from the celestial body than the assumed position.

b)

The observed position is closer to the celestial body than the assumed position.

c)

The observer's position is exactly at the celestial body's position.

d)

The observer's position is irrelevant to the celestial body's position.

68.

What is the purpose of the azimuth (Zn) in celestial navigation?

a)

To indicate the direction to the celestial body

b)

To measure the angular distance between celestial bodies

c)

To calculate the line of position (LoP)

d)

To determine the observer's latitude

69.

When solving the PZX triangle in celestial navigation, one of the sides, PZ, represents the observer's (a)   .

70.

What corrections are applied to a sextant reading to obtain the observed altitude (Ho)?

a)

Index error, Dip of the horizon, Refraction, Parallax.

b)

Declination, Latitude, Hour Angle.

c)

None, the sextant reading is used directly.

d)

Only Index error and Dip of the horizon.

71.

The intercept (a) helps navigators plot a _____ on a nautical chart to refine their position.

4 lines
72.

How is the intercept (a) affected when the observed altitude (Ho) is greater than the calculated altitude (Ha)?

a)

The intercept is positive

b)

The intercept is negative

c)

The intercept is zero

d)

The intercept cannot be determined

73.

In celestial navigation, the calculated altitude (Ha) is derived using sight reduction tables, the declination of the celestial body, and the _____.

4 lines
74.

What is the purpose of sight reduction tables in celestial navigation?

a)

To determine the calculated altitude (Ha) and azimuth (Zn) of a celestial body

b)

To measure the observed altitude (Ho) with a sextant

c)

To correct the compass deviation

d)

To plot the observer's line of position (LoP)

75.

What is the formula used to calculate the intercept (a)?

a)

a = Ho - Ha

b)

a = Ha - Ho

c)

a = Ho + Ha

d)

a = Ha - 2Ho

76.

What does the term "polar distance" refer to in the context of the PZX triangle?

a)

The side of the triangle representing 90° minus the declination (Dec) of the celestial body

b)

The distance between the celestial body and the observer

c)

The angle at the celestial pole (P)

d)

The angular distance from the observer's zenith to the celestial body

77.

A positive intercept (a) indicates that the observed position is closer to the celestial body than the assumed position.

(a)  

78.

Spherical trigonometry is unnecessary for solving the PZX triangle in celestial navigation.

(a)  

79.

The intercept (a) is the difference between the observed altitude (Ho) and the calculated altitude (Ha).

(a)  

80.

How does a navigator determine the local hour angle (LHA) of a celestial body?

a)

By calculating the angular distance west of the observer's meridian to the celestial body's meridian

b)

By measuring the angle between the celestial body and the zenith

c)

By subtracting the declination of the celestial body from the latitude

d)

By consulting the sight reduction tables

81.

Which of the following corrections must be applied to the sextant altitude (Hs) to obtain the observed altitude (Ho)?

a)

Index error

b)

Dip of the horizon

c)

Refraction

d)

Parallax

e)

Latitude correction

82.

Why is it important to calculate the intercept (a) in celestial navigation?

a)

To plot a line of position (LoP) on a nautical chart

b)

To measure the angle between two celestial bodies

c)

To determine the time of day

d)

To correct for compass variation

83.

What does a positive intercept (a) indicate in celestial navigation?

a)

The observed position is closer to the celestial body than the assumed position.

b)

The observed position is farther from the celestial body than the assumed position.

c)

The observed position is at the celestial body's position.

d)

The observer's position is irrelevant to the celestial body's position.

84.

What is the assumed position (AP) in celestial navigation?

a)

A convenient point near the observer's estimated location used for calculations

b)

The exact position of the observer

c)

The position of the celestial body at the time of observation

d)

The midpoint between the observed and calculated positions

85.

Which of the following is a step in determining the intercept (a) in celestial navigation?

a)

Calculate the calculated altitude (Ha) using sight reduction tables.

b)

Measure the azimuth of the celestial body.

c)

Determine the true heading of the observer.

d)

Adjust for compass deviation.

86.

What is the intercept (a) in celestial navigation defined as?

a)

The difference between the observed altitude (Ho) and the calculated altitude (Ha)

b)

The sum of the observed altitude (Ho) and the calculated altitude (Ha)

c)

The average of the observed altitude (Ho) and the calculated altitude (Ha)

d)

The product of the observed altitude (Ho) and the calculated altitude (Ha)

87.

What is the intercept (a) in celestial navigation?

a)

The difference between the observed altitude (Ho) and the calculated altitude (Ha).

b)

The observed altitude (Ho) without any corrections.

c)

The calculated altitude (Ha) derived using sight reduction tables.

d)

The azimuth of the celestial body.

88.

The formula for calculating the intercept in celestial navigation is a = (a)   - Ha.

89.

The observed altitude (Ho) is obtained directly from the sextant reading without any corrections.

(a)  

90.

What does the observed altitude (Ho) represent in celestial navigation?

a)

The altitude was measured with a sextant and corrected for various factors

b)

The theoretical altitude calculated based on the assumed position

c)

The angular distance between two celestial objects

d)

The altitude of the celestial body at its highest point

91.

How is the Sun's meridian altitude measured?

a)

By using a sextant to measure the angle of the Sun above the horizon at local noon

b)

By observing the Sun's declination directly

c)

By recording the time of sunrise and sunset

92.

What is the latitude formula when using the Sun's meridian altitude?

a)

Latitude = 90° - Altitude + Declination

b)

Latitude = Altitude + Declination

c)

Latitude = 90° + Altitude - Declination

93.

What is the latitude formula when using the Sun's meridian altitude?

a)

Latitude = 90° - Altitude + Declination

b)

Latitude = Altitude + Declination - 90°

c)

Latitude = 90° + Altitude - Declination

94.

Why is Polaris used to determine latitude in the Northern Hemisphere?

a)

Because Polaris is located almost directly above the Earth's North Pole, its altitude above the horizon closely matches the observer's latitude.

b)

Because Polaris moves quickly across the sky, making it easy to track.

c)

Because Polaris is the brightest star in the sky.

d)

Because Polaris is visible only during the day.

95.

How is the meridian altitude of the Sun measured?

a)

By using a sextant to measure the angle of the Sun above the horizon at its highest point, which is local noon.

b)

By observing the Sun's color and brightness.

c)

By measuring the time from sunrise to sunset.

d)

By using a thermometer to measure the Sun's heat.

96.

What is the role of a chronometer in navigating by the Sun's meridian altitude?

a)

To determine the exact time of local noon.

b)

To measure the Sun's altitude.

c)

To calculate the observer's latitude.

d)

To locate Polaris.

97.

What must be accounted for when using celestial observations to determine latitude?

a)

Atmospheric refraction and observer's height

b)

The Earth's rotation

c)

The color of the celestial object

d)

The observer's weight

98.

What does the observed altitude of Polaris indicate in the Northern Hemisphere?

a)

The observer's latitude

b)

The observer's longitude

c)

The observer's distance to the equator

99.

What is the observer's latitude if the Sun's meridian altitude is 70° and the Sun's declination is +15°?

a)

35° North

b)

75° North

c)

35° South

d)

75° South

100.

What is the purpose of an artificial horizon in celestial navigation?

a)

An artificial horizon is used when the natural horizon is not visible, providing a reference for angle measurements.

b)

An artificial horizon is used to measure the height of celestial bodies.

c)

An artificial horizon is used to simulate the night sky.

d)

An artificial horizon is used to determine time zones.

101.

What is the latitude formula when using the meridian altitude of the Sun?

a)

Latitude = Altitude + Declination

b)

Latitude = 90° - Altitude + Declination

c)

Latitude = Declination - Altitude

d)

Latitude = 90° + Altitude - Declination

102.

What is the main factor causing atmospheric refraction?

a)

The bending of light due to changes in air density

b)

The motion of celestial bodies.

c)

The observer's height above sea level.

d)

The magnetic field of the Earth.

103.

How can magnetic declination affect compass navigation?

a)

It causes the compass needle to point away from true north

b)

It adjusts the altitude of celestial bodies above the horizon

c)

It affects the appearance of Polaris in the sky

104.

How does atmospheric refraction affect celestial navigation?

a)

Atmospheric refraction bends light and alters the apparent position of celestial bodies, requiring corrections to ensure accurate latitude determination.

b)

Atmospheric refraction increases the brightness of celestial bodies.

c)

Atmospheric refraction does not affect celestial navigation.

d)

Atmospheric refraction is only relevant for terrestrial navigation.

105.

What is the role of atmospheric refraction in celestial navigation?

a)

It alters the apparent position of celestial bodies

b)

It corrects the altitude angle of celestial bodies

c)

It determines the declination of the Sun

106.

The latitude of an observer in the Northern Hemisphere can be determined by the altitude of the _____ above the horizon.

4 lines
107.

What is the significance of Polaris in determining latitude in the Northern Hemisphere?

a)

The altitude of Polaris above the horizon directly indicates the observer's latitude.

b)

Polaris is used to calculate the Sun's declination.

c)

Polaris indicates the local noon time directly.

d)

Polaris' position changes depending on the observer's longitude.

108.

When measuring the meridian altitude of the Sun, the angle is taken at (a)   , which is when the Sun is at its highest point in the sky.

109.

What is the observer's latitude if Polaris is observed at an altitude of 40° above the horizon?

a)

40° North

b)

50° North

c)

40° South

d)

50° South

110.

What is the role of a sextant in celestial navigation?

a)

A sextant is used to measure the angle of a celestial body above the horizon.

b)

A sextant is used to measure the temperature of a celestial body.

c)

A sextant is used to calculate the speed of a ship.

d)

A sextant is used to determine the time of day.

111.

The altitude of the Pole Star above the horizon directly indicates the observer's latitude in the Northern Hemisphere.

a)

True

b)

False

112.

What is the primary purpose of a chronometer in celestial navigation?

a)

To determine the exact time of local noon

b)

To measure the altitude of celestial bodies

c)

To locate Polaris

113.

Measuring the meridian altitude of the Sun requires knowledge of the Sun's declination to calculate the observer's latitude.

(a)  

114.

What instrument is commonly used to measure the altitude of the Sun during celestial navigation?

a)

Compass

b)

Chronometer

c)

Sextant

d)

Altimeter

115.

Which instrument is traditionally used to measure the meridian altitude of the Sun?

a)

Sextant

b)

Chronometer

c)

Telescope

116.

Atmospheric (a)   bends light and affects the apparent position of celestial bodies, requiring corrections during navigation.

117.

What celestial body is used to determine latitude directly in the Northern Hemisphere?

a)

Polaris

b)

Sun

c)

Moon

118.

What correction must be applied when measuring celestial altitude from a ship?

a)

Horizon dip correction

b)

Magnetic declination correction

c)

Atmospheric density correction

119.

Which instrument is typically used to measure the angle of the Sun above the horizon?

a)

Sextant

b)

Telescope

c)

Compass

d)

Chronometer

120.

What is the declination of the Sun?

a)

The angular distance of the Sun north or south of the celestial equator

b)

The angle between the Sun and the observer's zenith

c)

The altitude angle of the Sun above the horizon

121.

The latitude of an observer is determined by the angle between the celestial body and the horizon at local noon.

a)

True

b)

False

122.

What is the significance of the Sun's declination in calculating latitude?

a)

The Sun's declination is its angular distance north or south of the celestial equator and is required to calculate latitude when using the meridian altitude method.

b)

The Sun's declination is the angle of the Sun from the zenith.

c)

The Sun's declination is the time it takes to reach local noon.

d)

The Sun's declination is the brightness of the Sun.

123.

What is the main advantage of using Polaris for latitude determination?

a)

Polaris provides a direct and straightforward method to determine latitude in the Northern Hemisphere without requiring additional calculations.

b)

Polaris is visible in both the Northern and Southern Hemispheres.

c)

Polaris changes its position rapidly, making it easy to track.

d)

Polaris is the brightest star in the sky, making it easy to locate.

124.

Magnetic declination is the angle difference between true north and magnetic north, and it varies depending on the observer's location.

(a)  

125.

The (a)   is used to measure the angle of a celestial body above the horizon during celestial navigation.

126.

What correction is necessary when measuring the Sun's altitude from a ship?

a)

A dip correction to account for the observer's height above sea level

b)

A time correction for the ship's speed

c)

A color correction for the Sun's brightness

d)

A temperature correction for the Sun's heat

127.

What is latitude as defined in celestial navigation?

a)

Latitude is the angular distance of a point north or south of the Earth's equator, measured in degrees.

b)

Latitude is the same as longitude.

c)

Latitude is the distance in kilometers from the equator.

d)

Latitude is the angular distance of a point east or west of the prime meridian.

128.

What is the formula to calculate latitude using the Sun's meridian altitude?

a)

Latitude = 90° - Altitude + Declination

b)

Latitude = Altitude + Declination