WorksheetsBSME SET#5
Total questions: 95
Worksheet time: 32mins
Find the supplement of an angle whose compliment is 62°.
28°
118°
152°
none of these
A certain angle has a supplement five times its complement. Find the angle.
67.5°
157.5°
168.5°
186°
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.
15°
75°
90°
120°
The measure of 1½ revolutions counter-clockwise is:
540°
520°
+90°
-90°
The measure of 2.25 revolutions counterclockwise is:
-835°
-810°
805°
810°
Solve for θ: sin θ - sec θ + csc θ - tan 2θ = -0.0866
40°
41°
47°
43°
What are the exact values of the cosine and tangent trigonometric functions of acute angle A, given that sin A = 3/7?
cos A = 7/2√10 ; tan A = 2√10 /3
cos A = 2√10 /7 ; tan A = 3√10 /20
cos A = 2√10 /3 ; tan A = 7/2√10
cos A = 2√10 /3 ; tan A = 7√10 /20
Given three angles A, B, and C whose sum is 180°. If tan A + tan B + tan C = x, find the value of tan A × tan B × tan C.
1 - x
√x
x/2
x
What is the sine of 820°?
0.984
-0.866
0.866
-0.500
Csc 270° = ?
-√3
-1
√3
1
If coversine θ is 0.134, find the value of θ.
60°
45°
30°
20°
Solve for cos 72° if the given relationship is cos 2A = 2 cos²A - 1.
0.309
0.258
0.268
0.315
If sin 3A = cos 6B then:
A + B = 180°
A + 2B = 30°
A - 2B = 30°
A + B = 30°
Find the value of sin (arccos 15/17).
8/17
17/9
8/21
8/9
Find the value of cos [arcsin (1/3) + arctan (2/√5)].
(2/9)/(1 + √10)
(2/9)/(√10 - 11)
(2/9)/(√10 + 1)
(2/9)/(√10 - 1)
If sin 40° + sin 20° = sin θ, find the value of θ.
20°
80°
120°
60°
How many different values of x from 0° to 180° for the equation (2 sin x - 1)(cos x + 1) = 0?
A. 3
B. 0
C. 1
D. 2
For what value of θ (less than 2π) will the following equation be satisfied? sin²θ + 4 sin θ + 3 = 0
π
π/4
3π/2
π/2
Find the value of x in the equation csc x + cot x = 3.
A. π/4
B. π/3
C. π/2
D. π/5
If sec²A is 5/2, the quantity 1 - sin²A is equivalent to:
2.5
0.6
1.5
0.4
Find sin x if 2 sin x + 3 cos x - 2 = 0.
1 & -5/13
-1 & 5/13
1 & 5/13
-1 & -5/13
If sin A = 4/5, A in quadrant II, sin B = 7/25, B in quadrant I, find sin (A + B).
3/5
2/5
3/4
4/5
If sin A = 2.571x, cos A = 3.06x, and sin 2A = 3.939x, find the value of x.
0.350
0.250
0.100
0.150
If cos θ = √3 / 2, then find the value of x if x = 1 - tan²θ.
-2
-1/3
4/3
2/3
If sin θ - cos θ = -1/3, what is the value of sin 2θ?
1/3
1/9
8/9
4/9
If x cos θ + y sin θ = 1 and x sin θ - y cos θ = 3, what is the relationship between x and y?
A. x² + y² = 20
B. x² - y² = 5
C. x² + y² = 16
D. x² + y² = 10
If sin x + 1 / sin x = √2, then sin²x + 1 / sin²x is equal to:
√2
1
2
0
The equation 2 sin θ + 2 cos θ - 1 = √3 is:
an identity
a parametric equation
a conditional equation
a quadratic equation
If x + y = 90°, then (sin x tan y) / (sin y tan x) is equal to:
tan x
cos x
cot x
sin x
If cos θ = x / 2 then 1 - tan²θ is equal to:
(2x² + 4) / x²
(4 - 2x²) / x²
(2x² - 4) / x
(2x² - 4) / x²
Find the value in degrees of arccos (tan 24°).
61.48
62.35
63.56
arctan [2 cos (arcsin (√3 / 2))] is equal to:
π/3
π/4
π/6
π/2
Solve for x in the equation: arctan (2x) + arctan (x) = π/4
0.821
0.218
0.281
0.182
Solve for x from the given trigonometric equation: arctan (1 - x) + arctan (1 + x) = arctan 1/8
4
6
8
2
Solve for y if y = (1/sin x - 1/tan x)(1 + cos x)
sin x
cos x
tan x
sec²x
Solve for x: x = (tan θ + cot θ)² sin²θ - tan²θ
cos θ
1
2
Solve for x: x = 1 - (sin θ - cos θ)²
sin θ cos θ
-2 cos θ
cos 2θ
sin 2θ
Simplify cos⁴θ - sin⁴θ.
2
1
2 sin²θ + 1
2 cos²θ - 1
Solve for x: x = (1 - tan²a) / (1 + tan²a)
cos a
sin 2a
cos 2a
sin a
Which of the following is different from the others?
2 cos 2x - 1
cos 4x - sin 4x
cos 3x - sin 3x
1 - 2 sin 2x
Find the value of y: y = (1 + cos 2θ) tan θ
cos θ
sin θ
sin 2θ
cos 2θ
The equation 2 sinh x cosh x is equal to:
eˣ
e⁻ˣ
sinh 2x
cosh x
Simplifying the equation sin²θ (1 + cot²θ) gives:
1
sin²θ
sin²θ sec²θ
cos²θ
Find the value of sin (90° + A)
cos A
-cos A
sin A
-sin A
Which of the following expressions is equivalent to sin 2θ?
2 sin θ cos θ
sin²θ + cos²θ
cos²θ - sin²θ
sin θ cos θ
If tan θ = x², which of the following is incorrect?
sin θ = 1 / √(1 + x⁴)
sec θ = √(1 + x⁴)
cos θ = 1 / √(1 + x⁴)
csc θ = √(1 + x⁴) / x²
In an isosceles right triangle, the hypotenuse is how much longer than its sides?
2 times
√2 times
1.5 times
none of these
Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.
2.5 mils
2 mils
4 mils
1 mil
The angle or inclination of ascend of a road having 8.25% grade is ___ degrees.
5.12 degrees
4.72 degrees
1.86 degrees
4.27 degrees
The sides of a right triangle are in arithmetic progression whose common difference is 6 cm. Its area is:
216 cm²
270 cm²
360 cm²
144 cm²
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.
15 cm
16 cm
17 cm
18 cm
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 it be after 2 hours?
43.5
45.2
47.9
41.6
Two Sides of a triangle measures 6 cm. and 8 cm. and their included angle is 40°. Find the third side.
5.144 cm
5.263 cm
4.256 cm
5.645 cm
Given a triangle: C = 100°, a = 15, b = 20. Find c.
27
43
35
Given angle A = 32°, angle B = 70° and side C = 27 units. Solve for side A of the triangle.
24 units
10 units
14.63 units
12 units
In a triangle, find the side c if angle C = 100°, side b = 20, and side a = 15.
28
27
29
26
In triangle ABC, A = 45 degrees and angle C = 70 degrees. The side opposite angle C is 40 m. long. What is the side opposite angle A?
29.10 m
32.35 m
30.10 m
31.25 m
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 opposite the longest side?
93.74
94.74
91.74
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.
5.21 cm
3.78 cm
4.73 cm
6.25 cm
If AB = 15 m, BC = 18 m and CA = 24 m, find the point intersection of the angular bisector from the vertex C.
11.3
12.1
13.4
14.3
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?
36.8 m
37.1 m
36.3 m
37.4 m
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:
35.53
54.32
52.43
62.54
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
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:
100 m
130 m
125 m
115 m
From a point outside of an equilateral triangle, the distance to the vertices are 10m, 10m, and 18m. Find the dimension of the triangle.
25.63
45.68
19.64
12.25
Points A and B 1000m 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.
264 m
274 m
284 m
294 m
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?
After 4.36 hours
After 5.57 hours
After 2.13 hours
After 4.54 hours
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?
5/√2 meters
2/√5 meters
20 meters
√10 meters
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.
100 + 3√30
200 + √30
100√30/3
100√3/30
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.
8.67 m
7.53 m
7.02 m
8.09 m
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 at an inclination of 30° to the horizon, and reaching a point C, an observer finds that the angle ACB is 135°. The height of the mountain in feet is:
14386
12493
11672
11225
A 50-meter vertical tower casts a 62.3-meter shadow when the angle of elevation of the sun is 41.6°. The inclination of the ground is:
4.72°
4.33°
5.63°
5.17°
A vertical pole is 10 m from a building. When the angle of elevation of the sun is 45°, the pole cast a shadow on the building 1 m high. Find the height of the pole.
0 m
11 m
12 m
13 m
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 length of the pole?
52.43 m
54.23 m
53.25 m
53.24 m
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?
85.6 feet
143.97 feet
110.29 feet
92.53
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?
38.6 m
42.3 m
44.1 m
40.7 m
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?
271.6 m
265.4 m
259.2 m
277.9 m
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?
76.31 m
73.61 m
73.31 m
73.16
The angle of elevation of a point C from a point 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?
47.1 m
52.3 m
35.1 m
66.9 m
A rectangular piece of land 40m x 30m is to be crossed diagonally by a 10-m wide roadway. If the land cost 1500 per square meter, the cost of the roadway is:
401.10
60,165
601,650
651,500
A man improvises a temporary shield from the sun using a triangular piece of wood with
dimensions of 1.4m, 1.5m, and 1.3m. 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?
0.5 m²
0.27 m²
0.84 m²
0.95 m²
A rectangular piece of wood 4cm x 12cm tall is tilted at an angle of 45°. Find the
vertical distance between the lower corner and the upper corner.
4√2 cm
2√2 cm
8√2 cm
6√2 cm
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.
9.17 inches
8.23 inches
10.65 inches
11.25 inches
If the bearing of A from B is S 40° W, then the bearing of B from A is:
N 40° E
N 40°W
N 50°E
N 50°W
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 5º with
the horizontal Find the angle between the directions of the two paths.
13.21
18.74°
15.56°
17.22°
Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40°,
65°and 110°.
12.34 m²
14.89 m²
16.45 m²
15.27 m²
A right spherical triangle has an angle C = 90°, a = 50°and c = 80°. Find the side b.
45.33°
78.66°
74.33°
75.89°
If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at
120° East longitude?
6 PM
4 AM
4 PM
6 AM
An airplane flew from Manila (14° 36′N, 121° 05’ E ) at a course of S 30° E
maintaining a certain and following a great circle path. If its groundspeed is 350 knots,
after how many hours will it cross the equator?
2.87 hours
2.27 hours
3.17 hours
3.97 hours
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.
7856.2 nautical miles
5896.2 nautical miles
6326 2 nautical miles
6046.2 nautical miles
A at certain point on the ground, the tower at the top of a 20-m high building subtends
an angle of 45°. At another point on the ground 25 m closer the building, the tower
subtends an angle of 45°. Find the height of the tower.
124.75 m
87.45 m
154.32 m
101.85 m
A wooden flagpole is imbedded 3 m deep at corner A of a concrete horizontal slab
ABCD, square in form and measuring 20 ft on a side. A storm broke the flagpole at a
point one meter above the slab and inclined toward corner C in the direction of the
diagonal AC. The vertical angles observed at the center of the slab and at corner C to the
tip of the flagpole were 65 deg and 35 deg respectively. What is the total length of the
flagpole above the slab in yards?
5.61
16. 83
4.32
12.38
From the third floor window of a building, the angle of Depression of an object on the
ground is 35° 58’, while from a sixth floor window, 9.75 m above the first point of
observation the angle of depression is 58° 35’. How far is the object from the building?
11.9 m
10.7 m
9.3 m
15.3 m
The sides of a triangle are 18 cm, 24 cm and 34 cm, respectively. Find the length of the
median to the 24-cm side, in cm.
24.4
21.9
23.4
20.4
In the spherical triangle ABC, A = 116° 19’, B = 55° 30′, and C80° 37’. What is the
value of side a.
115.57°
113.21°
119.64°
115.65°
