Free Printable Pinoybix

1.

If Greenwich Mean Time (GMT) is 6 A.M., what is the time at a place located 30° East longitude?

a)

7 A.M.

b)

8 A.M.

c)

9 A.M.

d)

4 A.M.

2.

If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?

a)

1 hour and 12 minutes

b)

1 hour and 5 minutes

c)

1 hour and 8 minutes

d)

1 hour and 10 minutes

3.

One degree on the equator of the earth is equivalent to?

a)

1 minute

b)

4 minute

c)

30 minute

d)

1 hour

4.

A spherical triangle ABC as an angle C = 90° and sides a = 50º and c = 80°. Find the value of “b” in degrees.

a)

73.22°

b)

74.33°

c)

75.44°

d)

76.55°

5.

Solve the remaining side of the spherical triangle whose given parts are A = B = 80° and a = b = 89°.

a)

158° 12’

b)

162° 21’

c)

168° 31’

d)

172° 12’

6.

Solve for the side b of a right spherical triangle ABC whose parts are a = 46°, c = 75° and C = 90°.

a)

72°

b)

68°

c)

48°

d)

74°

7.

Given the right spherical triangle whose given parts are a = 82°, b = 62° and c = 90°. What is the value of the side opposite the right angle?

a)

84° 30’

b)

84° 45’

c)

86° 15’

d)

85° 15’

8.

Determine the value of the angle B of an isosceles spherical triangle ABC whose given parts are b = c = 54° 28’ and a = 92° 30’.

a)

89° 45’

b)

55° 45’

c)

84° 25’

d)

41° 45’

9.

Solve for angle A in the spherical triangle ABC, given a = 106º 25’, c = 42° 16’ and B = 114° 53’.

a)

45° 54’

b)

80° 42’

c)

97° 09’

d)

72° 43’

10.

Solve for angle C of the oblique triangle ABC given, a = 80°, c = 115° and A = 72º

a)

61°

b)

85°

c)

95°

d)

119°

11.

Determine the spherical excess of the spherical triangle ABC given a = 56°, b = 65º and c = 78°.

a)

33° 33’

b)

68° 37’

c)

91° 57’

d)

98° 45’

12.

What is the spherical excess of a spherical triangle whose angles are all right angles?

a)

45°

b)

90°

c)

60°

d)

30°

13.

The area of a spherical triangle ABC whose parts are A = 93º 40’, B = 64° 12’, C = 116º 51’ and the radius of the sphere is 100 m is?

a)

15613 sq. m.

b)

16531 sq. m.

c)

18645 sq. m.

d)

25612 sq. m.

14.

A spherical triangle has an area of 327.25 sq. km. What is the radius of the sphere if its spherical excess is 30º?

a)

20 km

b)

22 km

c)

25 km

d)

28 km

15.

A ship on a certain day is at latitude 20º N and longitude 140º E. After sailing for 150 hours at a uniform speed along a great circle route, it reaches a point at latitude 10º S and longitude 170º W. If the radius of the earth is 3959 miles, find the speed in miles per hour.

a)

17.4

b)

15.4

c)

16.4

d)

19.4

16.

Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40°, 65°, and 110°.

a)

12.34 sq. m.

b)

14.89 sq. m.

c)

16.45 sq. m.

d)

15.27 sq. m.

17.

A right spherical triangle has an angle C = 90°, a = 50°, and c = 80°. Find the side b.

a)

45.33°

b)

78.66°

c)

74.33°

d)

75.89°

18.

If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at 120° East longitude?

a)

6 p.m.

b)

4 am

c)

4 p.m.

d)

6 am

19.

An airplane flew from Manila (14° 36’N, 121° 05’E) at a course of S 30° E maintaining a certain altitude and following a great circle path. If its groundspeed is 350 knots, after how many hours will it cross the equator?

a)

2.87 hours

b)

2.27 hours

c)

3.17 hours

d)

3.97 hours

20.

Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14° 36’N latitude and 121° 05’ E longitude. San Francisco is situated at 37° 48’ N latitude and 122° 24’ W longitude.

a)

7856.2 nautical miles

b)

5896.2 nautical miles

c)

6326.2 nautical miles

d)

6046.2 nautical miles

21.

Find the supplement of an angle whose compliment is 62°.

a)

28°

b)

118°

c)

152°

d)

None of these

22.

A certain angle has a supplement 5 times its compliment. Find the angle.

a)

67.5°

b)

157.5°

c)

168.5°

d)

186°

23.

The sum of the two interior angles of the triangle is equal to the third angle and the difference of the two angles is equal to 2/3 of the third angle. Find the third angle.

a)

15°

b)

75°

c)

90°

d)

120°

24.

The measure 0f $1\frac{1}{2}$ revolutions counter-clockwise is:

a)

540°

b)

520°

c)

+90°

d)

-90°

25.

The measure of 2.25 revolutions counterclockwise is:

a)

-835°

b)

-810°

c)

805°

d)

810°

26.

Solve for $θ:\ \sinθ–\secθ+\cscθ–\tan2θ=–0.0866$

a)

40°

b)

41°

c)

47°

d)

43°

27.

What are the exact values of the cosine and tangent trigonometric functions of acute angle A, given that $\sin\ A=\ \frac{3}{7\ }\ \ ?$

a)

$\cos\ A=\frac{7}{2}\sqrt{10}\ ;\ \tan A\ =\ 2\sqrt{\frac{10}{3}}$

b)

$\cos\ A=2\sqrt{\frac{10}{7}}\ ;\ \tan A\ =\ 3\sqrt{\frac{10}{20}}$

c)

$\cos\ A=2\sqrt{\frac{10}{3}}\ ;\ \tan A\ =\ \frac{7}{2}\sqrt{10}$

d)

$\cos\ A=2\sqrt{\frac{10}{3}}\ ;\ \tan A\ =\ \frac{7}{2}\sqrt{\frac{10}{20}}$

28.

Given three angles A, B, and C whose sum is 180°. If the $\tan A+\tan B+\tan C=x$ , find the value of tan $A\times\tan B\times\tan C.$

a)

$1-x$

b)

$\sqrt{x}$

c)

$\frac{x}{2}$

d)

$x$

29.

What is the sine of 820°?

a)

0.984

b)

-0.866

c)

0.866

d)

-0.500

30.

csc 270° = ?

a)

$-\sqrt{3}$

b)

$-1$

c)

$\sqrt{3}$

d)

$1$

31.

If coversine Ѳ is 0.134, find the value of Ѳ.

a)

60°

b)

45°

c)

30°

d)

20°

32.

Solve for cos 72° if the given relationship is cos 2A = 2 cos2 A – 1.c

a)

0.309

b)

0.258

c)

0.268

d)

0.315

33.

If sin 3A = cos 6B then:

a)

A + B = 180°

b)

A + 2B = 30°

c)

A – 2B = 30°

d)

A + B = 30°

34.

Find the value of $\sin\left(ar\cos\ \frac{15}{17}\right)$

a)

$\frac{8}{17}$

b)

$\frac{17}{9}$

c)

$\frac{8}{21}$

d)

$\frac{8}{9}$

35.

Find the value of
$\cos\left[\arcsin\ \left(\frac{1}{3}\right)+\arctan\left(\frac{2}{\sqrt{5}}\right)\right]$

a)

$\left(\frac{2}{9}\right)\left(1+\sqrt{10}\right)$

b)

$\left(\frac{2}{9}\right)\left(\sqrt{10}\ -\ 11\right)$

c)

$\left(\frac{2}{9}\right)\left(\sqrt{10}+1\right)$

d)

$\left(\frac{2}{9}\right)\left(\sqrt{10}-1\right)$

36.

If sin 40° + sin 20° = sin Ѳ, find the value of Ѳ.

a)

20°

b)

80°

c)

120°

d)

60°

37.

How many different value of x from 0° to 180° for the equation (2sin x – 1)(cos x + 1) = 0?

a)

3

b)

0

c)

1

d)

2

38.

For what value of Ѳ (less than 2π) will the following equation be satisfied?

sin2 Ѳ + 4sinѲ + 3 = 0

a)

n

b)

$\frac{n}{4}$

c)

$\frac{3n}{2}$

d)

$\frac{n}{2}$

39.

Find the value of x in the equation csc x + cot x = 3.

a)

\frac{n}{4}

b)

$\frac{n}{3}$

c)

$\frac{n}{2}$

d)

$\frac{n}{5}$

40.

If sec2 A is $\frac{5}{2}$ the quantity 1 – sin2 A is equivalent to:

a)

$2.5$

b)

$0.6$

c)

$1.5$

d)

$0.4$

41.

Find sin x if 2 sin x + 3 cos x – 2 = 0.

a)

$1\ \&\ -\frac{5}{13}$

b)

$-1\ \&\ \frac{5}{13}$

c)

$1\ \&\ \frac{5}{13}$

d)

$-1\ \&\ -\frac{5}{13}$

42.

If $\sin\ A\ =\ \frac{4}{5}$ , A in quadrant II, $\sin\ B=\frac{7}{25}$ , B in quadrant I, find $\sin\ \left(A+B\right)$ .

a)

$\frac{3}{5}$

b)

$\frac{2}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{5}$

43.

If sin A = 2.571x, cos A = 3.06, and sin 2A = 3.939x, find the value of x.

a)

0.350

b)

0.250

c)

0.100

d)

0.150

44.

If $\cos\Theta\ =\ \sqrt{\frac{3}{2}}$ , what is the value of x if x = 1 – tan2 Ѳ.

a)

$-2$

b)

$-\frac{1}{3}$

c)

$\frac{4}{3}$

d)

$\frac{2}{3}$

45.

If

\sin\Theta\ -\ \cos\Theta=-\frac{1}{3}

what is the value of sin 2 Ѳ?

a)

\frac{1}{3}

b)

$\frac{1}{9}$

c)

$\frac{8}{9}$

d)

$\frac{4}{9}$

46.

If x cos Ѳ + y sin Ѳ = 1 and x sin Ѳ – y cos Ѳ = 3, what is the relationship between x and y?

a)

x^2+y^2=20

b)

$x^2-y^2=5$

c)

$x^2+y^2=16$

d)

$x^2+y^2=10$

47.

If $\frac{\sin x+1}{\sin x}=\sqrt{2}$ . then $\frac{\sin2\ x+1}{\sin2\ x}$ is equal to :

a)

$\sqrt{2}$

b)

$1$

c)

$2$

d)

$0$

48.

The equation 2 sin Ѳ + 2 cos Ѳ – 1 = $\sqrt{3}$ is:

a)

An identity

b)

A parametric equation

c)

A conditional equation

d)

A quadratic equation

49.

If x + y = 90°, then $\left(\frac{\left(\sin\ x\ \tan\ y\right)}{\left(\sin\ y\ \tan\ x\right)}\right)$ is equal to:

a)

tan x

b)

cos x

c)

cot x

d)

sin x

50.

if cos Ѳ = $\frac{x}{2}$ then 1 – tan2 Ѳ is equal to:

a)

$\frac{\left(2\times2+4\right)}{x^2}$

b)

$\frac{\left(4-2\times4\right)}{x^2}$

c)

$\frac{\left(2\times2-4\right)}{x^{ }}$

d)

$\frac{\left(2\times2-4\right)}{x^2}$

51.

Find the value in degrees of arcos (tan 24°).

a)

61.48

b)

62.35

c)

63.56

d)

60.84

52.

arctan $\left[2\cos\left(\frac{3}{2}\right)\right]$ is equal to :

a)

$\frac{n}{3}$

b)

$\frac{n}{4}$

c)

$\frac{n}{6}$

d)

$\frac{n}{2}$

53.

Solve for x in the equation: arctan (2x) + arctan (x) = $\frac{n}{4}$

a)

0.821

b)

0.218

c)

0.281

d)

0.182

54.

Solve for x from the given trigonometric equation:
arctan (1 – x) + arctan (1 + x) = arctan $\frac{1}{8}$

a)

4

b)

6

c)

8

d)

2

55.

Solve for y if

y = $\left(\frac{1}{\sin x}\ -\ \frac{1}{\tan x}\right)$ (1 + cos x)

a)

sin x

b)

cos x

c)

tan x

d)

sec2 x

56.

Solve for x: x = (tan θ + cot θ)2 sin2 θ – tan 2 θ.

a)

sin θ

b)

cos θ

c)

1

d)

2

57.

Solve for x: x = 1 – (sin θ – cos θ)2

a)

sin θ cos θ

b)

-2 cos θ

c)

cos 2θ

d)

sin 2θ

58.

Simplify cos4 θ – sin4 θ

a)

2

b)

1

c)

2 sin2 θ + 1

d)

2 sin2 θ - 1

59.

Solve for x: $x=\left(\frac{\left(1-\tan2a\right)}{\left(1+\tan2a\right)}\right)$

a)

cos a

b)

sin 2a

c)

cos 2a

d)

sin a

60.

which of the following is different from the others?

a)

2 cos 2x – 1

b)

cos 4x – sin 4x

c)

cos 3x – sin 3x

d)

1 – 2 sin 2x

61.

Find the value of y: y = (1 + cos 2θ) tan θ.

a)

cos θ

b)

sin θ

c)

sin 2θ

d)

cos 2θ

62.

The equation 2 sinh x cosh x is equal to:

a)

ex

b)

e-x

c)

sinh 2x

d)

cosh 2x

63.

Simplifying the equation sin2 θ(1 + cot2 θ)

a)

1

b)

sin2 θ

c)

sin2 θ sec2 θ

d)

sin2 θ

64.

If tan θ = x2, which of the following is incorrect?

a)

$\sin\ \theta=\ \frac{1}{\sqrt{\left(1+x^4\right)}}$

b)

$\sec\theta\ =\ \sqrt{\left(1+x^4\right)}$

c)

$\cos s\theta=\ \frac{1}{\sqrt{\left(1+x^4\right)}}$

d)

$\csc\ \theta=\ \frac{\sqrt{\left(1+x^4\right)}}{x^2}$

65.

In an isosceles right triangle, the hypotenuse is how much longer than its sides?

a)

2 times

b)

$\sqrt{2}$ times

c)

1.5 times

d)

None of these

66.

Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.

a)

2.5 mils

b)

2 mils

c)

4 mils

d)

1 mil

67.

The angle or inclination of ascend of a road having 8.25% grade is _____degrees.

a)

5.12 degrees

b)

4.72 degrees

c)

1.86 degrees

d)

4.27 degrees

68.

The sides of a right triangle is in arithmetic progression whose common difference if 6 cm. its area is:

a)

216 $cm^2$

b)

270 $cm^2$

c)

360 $cm^2$

d)

144 $cm^2$

69.

The hypotenuse of a right triangle is 34 cm. Find the length of the shortest leg if it is 14 cm shorter than the other leg.

a)

15 cm

b)

16 cm

c)

17 cm

d)

18 cm

70.

A truck travels from point M northward for 30 min. then eastward for one hour, then shifted N 30° W. if the constant speed is 40 Kph, how far directly from M, in km. will be it after 2 hours?

a)

43.5

b)

45.2

c)

47.9

d)

41.6

71.

Two sides of a triangle measures 6 cm. and 8 cm. and their included angle is 40°. Find the third side.

a)

5.144 cm

b)

5.263 cm

c)

4.256 cm

d)

5.645 cm

72.

Given a triangle: C = 100°, a = 15, b = 20. Find c:

a)

34

b)

27

c)

43

d)

35

73.

Given angle A = 32°, angle B = 70°, and side c = 27 units. Solve for side a of the triangle.

a)

24 units

b)

10 units

c)

14.63 units

d)

12 units

74.

n a triangle, find the side c if the angle C = 100°, side b = 20, and side a = 15.

a)

28

b)

27

c)

29

d)

26

75.

Two sides of a triangle are 50 m. and 60 m. long. The angle included between these sides is 30 degrees. What is the interior angle (in degrees) opposite the longest side?

a)

92.74

b)

93.74

c)

94.74

d)

91.74

76.

The sides of a triangle ABC are AB = 15 cm, BC = 18 cm, and CA = 24 cm. Determine the distance from the point of intersection of the angular bisectors to side AB.

a)

5.21 cm

b)

3.78 cm

c)

4.73 cm

d)

6.25 cm

77.

If AB = 15 m, BC = 18 m and CA = 24 m, find the point of intersection of the angular bisector from the vertex C.

a)

11.3

b)

12.1

c)

13.4

d)

14.3

78.

In triangle ABC, angle C = 70 degrees; angle A = 45 degrees; AB = 40 m. what is the length of the median drawn from vertex A to side BC?

a)

36.8 meters

b)

37.1 meters

c)

36.3 meters

d)

37.4 meters

79.

The area of the triangle whose angles are 61°9’32”, 34°14’46”, and 84°35’42” is 680.60. the length of the longest side is:

a)

35.53

b)

54.32

c)

52.43

d)

62.54

80.

Given a triangle ABC whose angles are A = 40°, B = 95° and side b = 30 cm. find the length of the bisector of angle C.

a)

21.74 cm

b)

22.35 cm

c)

20.45 cm

d)

20.98 cm

81.

The sides of a triangular lot are 130 m, 180 m, and 190 m. the lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. The length of this dividing line is:

a)

100 meters

b)

130 meters

c)

125 meters

d)

115 meters

82.

From a point outside of an equilateral triangle, the distances to the vertices are 10m, 10m, and 18m. Find the dimension of the triangle.

a)

25.63

b)

45.68

c)

19.94

d)

12.25

83.

Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32 degrees N of W and from B the bearing of C is 26 degrees N of E. Approximate the shortest distance of tower C to the highway.

a)

264 meters

b)

274 meters

c)

284 meters

d)

294 meters

84.

An airplane leaves an aircraft carrier and flies South at 350 mph. The carrier travels S 30° E at 25 mph. If the wireless communication range of the airplane is 700 miles, when will it lose contact with the carrier?

a)

after 4.36 hours

b)

after 5.57 hours

c)

after 2.13 hours

d)

after 4.54 hours

85.

A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue?

a)

$5\sqrt{2}$ meter

b)

$2\sqrt{5}$ meter

c)

$20$ meter

d)

$\sqrt{10}$ meter

86.

From the top of a building 100 m high, the angle of depression of a point A due East of it is 30°. From a point B due South of the building, the angle of elevation of the top is 60°. Find the distance AB.

a)

$100+3\sqrt{30}$

b)

$200–\sqrt{30}$

c)

$\frac{\left(100(\sqrt{30}\right)}{3}$

d)

$\frac{100\sqrt{3}}{30}$

87.

An observer found the angle of elevation of the top of the tree to be 27°. After moving 10m closer (on the same vertical and horizontal plane as the tree), the angle of elevation becomes 54°. Find the height of the tree.

a)

8.65 meters

b)

7.53 meters

c)

7.02 meters

d)

8.09 meters

88.

From a point A at the foot of the mountain, the angle of elevation of the top B is 60°. After ascending the mountain one (1) mile to an inclination of 30° to the horizon, and reaching a point C, an observer finds that the angle ACB is 135°.

a)

14386

b)

12493

c)

11672

d)

11223

89.

A vertical pole is 10 m from a building. When the angle of elevation of the sum is 45°, the pole cast a shadow on the building 1 m high. Find the height of the pole.

a)

0 meter

b)

11 meter

c)

12 meter

d)

13 meter

90.

A pole cast a shadow of 15 meters long when the angle of elevation of the sun is 61°. If the pole has leaned 15° from the vertical directly toward the sun, what is the length of the pole?

a)

52.43 meters

b)

54.23 meters

c)

53.25 meters

d)

53.24 meters

91.

An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A and B, which are 50 ft. apart, at the same elevation on a direct line with the tower. The vertical angle at point A is 30° and at point B is 40°. What is the height of the tower?

a)

85.6 feet

b)

143.97 feet

c)

110.29 feet

d)

92.54 feet

92.

From the top of tower A, the angle of elevation of the top of the tower B is 46°. From the foot of tower B the angle of elevation of the top of tower A is 28°. Both towers are on a level ground. If the height of tower B is 120m, how high is tower A in m?

a)

38.6

b)

42.3

c)

44.1

d)

40.7

93.

Points A and B are 100 m apart and are on the same elevation as the foot of a building. The angles of elevation of the top of the building from points A and B are 21° and 32°, respectively. How far is A from the building in m?

a)

271.6

b)

265.4

c)

259.2

d)

277.9

94.

A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m. nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?

a)

76.31 meters

b)

73.61 meters

c)

73.31 meters

d)

73.16 meters

95.

The angle of elevation of a point C from a pint B is 29°42’; the angle of elevation of C from another point A 31.2 m directly below B is 59°23’. How high is C from the horizontal line through A?

a)

47.1 meters

b)

52.3 meters

c)

35.1 meters

d)

66.9 meters

96.

A rectangular piece of land 40m x 30m is to be crossed diagonally by a 10-m wide roadway. If the land cost P1,500.00 per square meter, the cost of the roadway is:

a)

P401.10

b)

P60,165.00

c)

P601,650.00

d)

651,500.00

97.

A man improvises a temporary shield from the sun using a triangular piece of wood with dimensions of 1.4m, 1.5 m, and 1.3 m. with the longer side lying horizontally on the ground, he props up the other corner of the triangle with a vertical pole 0.9m long. What would be the area of the shadow on the ground when the sun is vertically overhead?

a)

0.5 $m^2$

b)

0.75 $m^2$

c)

0.84 $m^2$

d)

0.95 $m^2$

98.

A rectangular piece of wood 4 cm x 12 cm tall is titled at an angle of 45°. Find the vertical distance between the lower corner and the upper corner.

a)

$4\sqrt{2}\ cm$

b)

$2\sqrt{2}\ cm$

c)

$8\sqrt{2}\ cm$

d)

$6\sqrt{2}\ cm$

99.

A clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour hand is 6 inches long. The plane of rotation of the minute hand is 2 inches above the plane of rotation of the hour hand. Find the distance between the tips of the hands at 5:40 AM.

a)

9.17 inches

b)

8.23 inches

c)

10.65 inches

d)

11.25 inches

100.

If the bearing of A from B is 40° W, then the bearing of B from A is:

a)

N 40° E

b)

N 40° W

c)

N 50° E

d)

N 50° W

101.

A plane hillside is inclined at an angle of 28° with the horizontal. A man wearing skis can climb this hillside by following a straight path inclined at an angle of 12° to the horizontal, but one without skis must follow a path inclined at an angle of only 5° with the horizontal. Find the angle between the directions of the two paths.

a)

13.21°

b)

18.74°

c)

15.56°

d)

17.22°

102.

Sin (B – A) is equal to _______, when B = 270 degrees and A is an acute angle.

a)

– cos A

b)

cos A

c)

– sin A

d)

sin A

103.

If sec2 A is $\frac{5}{2}$ the quantity

1 – sin2 A is equivalent to?

a)

2.5

b)

1.5

c)

0.4

d)

0.6

104.

(cos A)4 – (sin A)4 is equal to ______.

a)

cos 4A

b)

cos 2A

c)

sin 2A

d)

sin 4A

105.

Of what quadrant is A, if sec A is positive and csc A is negative?

a)

IV

b)

II

c)

III

d)

I

106.

Angles are measured from the positive horizontal axis, and the positive direction is counter clockwise. What are the values of sin B and cos B in the 4th quadrant?

a)

sin B > 0 and cos B < 0

b)

sin B < 0 and cos B < 0

c)

sin B > 0 and cos B > 0

d)

sin B < 0 and cos B > 0-`

107.

$\csc52\degree$ is equal to

a)

$\cos\ 20\degree$

b)

$\csc\ 20\degree$

c)

$\tan\ 20\degree$

d)

$\sin\ 20\degree$

108.

Solve for θ in the following equation: Sin 2θ = cos θ

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

d)

$15\degree$

109.

If sin 3A = cos 6B, then

a)

A + B = $90\degree$

b)

A + 2B = $30\degree$

c)

A + B =

180\degree

d)

None of these

110.

Solve for x, if tan 3x = 5 tan x.

a)

$20.705\degree$

b)

$30.705\degree$

c)

$35.705\degree$

d)

$15.705\degree$

111.

If sin x cos x + sin 2x = 1, what are the values of x?

a)

$32.2\degree\ ,\ 69.3\degree$

b)

$-20.67\degree\ ,\ 69.3\degree$

c)

$20.90\degree\ ,\ 69.1\degree$

d)

$-32.2\degree\ ,\ 69.3\degree$

112.

Solve for G is csc (11G – 16 degrees) = sec (5G + 26 degrees).

a)

7 degrees

b)

5 degrees

c)

6 degrees

d)

4 degrees

113.

Find the value of A between $270\degree$ $360\degree$
if sin 2 A – sin A = 1.

a)

$300\degree$

b)

$320\degree$

c)

$310\degree$

d)

$330\degree$

114.

If cos 65o + cos 55o = cos θ, find the θ in radians.

a)

0.765

b)

0.087

c)

1.213

d)

1.421

115.

Find the value of $\frac{\sin\left(\arccos15\right)}{17}$

a)

$\frac{8}{11}$

b)

$\frac{8}{19}$

c)

$\frac{8}{15}$

d)

$\frac{8}{17}$

116.

The sine of a certain angle is 0.6, calculate the cotangent of the angle.

a)

$\frac{4}{3}$

b)

$\frac{5}{4}$

c)

$\frac{4}{5}$

d)

$\frac{3}{4}$

117.

If $\sec2A=\frac{1}{\sin13A}$ , determine the angle of aA in degress.

a)

$5\degree$

b)

$6\degree$

c)

$3\degree$

d)

$7\degree$

118.

If tan x= $\frac{1}{2}$ , tan y= $\frac{1}{3}$ , what is the value of tan (x + y) ?

a)

$\frac{1}{2}$

b)

$\frac{1}{6}$

c)

2

d)

1

119.

Find the value of y in the given: y = (1 + cos 2θ) tan θ.

a)

sin θ

b)

cos θ

c)

sin 2θ

d)

cos 2θ

120.

Find the value of $\frac{\sin\theta+\cos\theta\tan\theta}{\cos\theta}$

a)

2 sin θ

b)

2 cos θ

c)

2 tan θ

d)

2 cot θ

121.

Simplify the equation sin2 θ (1 + cot2 θ)

a)

1

b)

sin2 θ

c)

sin2 θ sec2 θ

d)

sec2 θ

122.

Simplify the expression sec θ – (sec θ) sin2 θ

a)

cos2 θ

b)

cos θ

c)

sin2 θ

d)

sin θ

123.

$\arctan\ \left[2\ \cos\ \left(\frac{\arcsin\ \left(\frac{31}{2}\right)}{2}\right)\right]$

is equal tp:

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{2}$

124.

Evaluate arccot [2cos (arcsin 0.5)]

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

d)

$90\degree$

125.

Solve for x in the given equation:

Arc tan (2x) + arc tan (x) = $\frac{n}{4}$

a)

0.149

b)

0.281

c)

0.421

d)

0.316

126.

Solve for x in the equation:

arc tan (x + 1) + arc tan (x – 1) = arc tan (12).

a)

1.5

b)

1.34

c)

1.20

d)

1.25

127.

Solve for A for the given equation cos2 A = 1 – cos2 A.

a)

45, 125, 225, 335 degrees

b)

45, 125, 225, 315 degrees

c)

45, 135, 225, 315 degrees

d)

45, 150, 220, 315 degrees

128.

Evaluate the following: $\frac{\sin0\degree+\sin2\degree+\sin3\degree+\cdot\cdot\cdot+\sin89\degree+\sin90\degree}{\cos0\degree+\cos1\degree+\cos2\degree+\cdot\cdot\cdot+\cos89\degree+\cos90\degree}$

a)

1

b)

0

c)

45.5

d)

10

129.

Simplify the following: $\frac{\cos A+\cos B}{\sin A-\sin A}\ +\ \frac{\sin A+\sin B}{\cos A-\cos B}$

a)

0

b)

sin A

c)

1

d)

cos A

130.

Evaluate: $\frac{2\sin\theta\cos\theta-\cos\theta}{1-\sin\theta+\sin^2\theta-\cos^2\theta}$

a)

sin θ

b)

cos θ

c)

tan θ

d)

cot θ

131.

Solve for the value of “A” when sin A = 3.5x and cos A = 5.5x.

a)

32.47°

b)

33.68°

c)

34.12°

d)

35.21°

132.

If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x?

a)

0.265

b)

0.256

c)

0.562

d)

0.625

133.

If coversed sin θ = 0.134, find the value of θ.

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

d)

$90\degree$

134.

A man standing on a 48.5 meter building high, has an eyesight height of 1.5 m from the top of the building, took a depression reading from the top of another nearby building and nearest wall, which are 50° and 80° respectively. Find the height of the nearby building in meters. The man is standing at the edge of the building and both buildings lie on the same horizontal plane.

a)

39.49

b)

35.50

c)

30.74

d)

42.55

135.

Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32° W of N and from B the bearing of C is 26° N of E. Approximate the shortest distance of tower C to the highway.

a)

364 m

b)

374 m

c)

384 m

d)

394 m

136.

Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the triangles differ by 21 square units.

a)

6 and 12

b)

3 and 9

c)

5 and 11

d)

4 and 10

137.

A ship started sailing S 42°35’ W at the rate of 5kph. After 2 hours, ship B started at the same port going N 46°20’W at the rate of 7 kph. After how many hours will the second ship be exactly north of ship A?

a)

3.68

b)

4.03

c)

5.12

d)

4.83

138.

An aerolift airplane can fly at an airspeed of 300 mph. If there is a wind blowing towards the cast at 50mph, what should be the plane’s compass heading in order for its course to be 30°? What will be the plane’s ground speed if it flies in this course?

a)

19.7, 307.4 mph

b)

20.1, 309.4 mph

c)

21.7, 321.8 mph

d)

22.3, 319.2 mph

139.

A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower?

a)

76.31 m

b)

73.31 m

c)

73.16 m

d)

73.61 m

140.

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° from the vertical directly towards the sun, determine the length of the pole.

a)

54.23 m

b)

48.23 m

c)

42.44 m

d)

46.21 m

141.

When supporting a pole is fastened to it 20 feet from the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole.

a)

24 ft, 53.13°

b)

24 ft, 36.87°

c)

24 ft, 53.13°

d)

25 ft, 36.87°

142.

The angle of elevation of the top of tower B from the top of tower A is 28° and the angle of the elevation of the top of tower A from the base of tower B is 46°. The two towers lie in the same horizontal plane. If the height of tower B is 120 m, find the height of tower A.

a)

66.3 m

b)

79.3 m

c)

87.2 m

d)

90.7 m

143.

Points A and B are 100 m apart and are of the same elevation as the foot of a building. The angles of elevation of the top of the building from points A and B are 21° and 32° respectively. How far is A from the building in meters.?

a)

259.28

b)

265.42

c)

271.64

d)

277.29

144.

The captain of a ship views the top of a lighthouse at an angle of 60° with the horizontal at an elevation of 6 meters above sea level. Five minutes later, the same captain of the ship views the top of the same lighthouse at an angle of 30° with the horizontal. Determine the speed of the ship if the lighthouse is known to be 50 meters above sea level.

a)

0.265 m/sec

b)

0.155 m/sec

c)

0.169 m/sec

d)

0.210 m/sec

145.

An observer wishes to determine the height of a tower. He takes sights at the top of the tower from A and B, which are 50 feet apart, at the same elevation on a direct line with the tower. The vertical angle at point A is 30° and at point B is 40°. What is the height of the tower?

a)

85.60 feet

b)

92.54 feet

c)

110.29 feet

d)

143.97 feet

146.

A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13° and 35° respectively. The height of the tower is 50 m. Find the height of the monument.

a)

29.13 m

b)

30.11 m

c)

32.12 m

d)

33.51 m

147.

If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.

a)

34.64 cm

b)

64.12 cm

c)

36.44 cm

d)

32.10 cm

148.

The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26°. What is the third side?

a)

197.49 m

b)

218.61 m

c)

341.78 m

d)

282.15 m

149.

The sides of a triangular lot are 130 m., 180 m and 190 m. the lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line.

a)

120 m

b)

130 m

c)

125 m

d)

128 m

150.

The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle?

a)

73,250 sq. units

b)

10,250 sq. units

c)

14,586 sq. units

d)

11,260 sq. units

151.

The sides of a triangle are 8, 15 and 17 units. If each side is doubled, how many square units will the area of the new triangle be?

a)

240

b)

420

c)

320

d)

200

Pinoybix - Trigonometry

Total questions: 151

Worksheet time: 8hrs 33mins

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