Trigonometric Ratios, Heights and Distances - One Line Questions
1.
If tan(theta) = 3/4, what is the value of (sin(theta) + cos(theta)) / (sin(theta) - cos(theta))? —
-7
2.
If tan(theta) = √3, what is the value of cot(theta)? —
1/√3
3.
If sin(theta) = 2/3, what is the value of cos(theta) for an acute angle theta? —
√5/3
4.
What is the value of sin²(A) + cos²(A) + tan²(A) - sec²(A)? —
0
5.
What is the value of sin²(theta) + cos²(theta)? —
1
6.
What is the value of sec²(theta) - tan²(theta)? —
1
7.
What is the value of sin(0°) + cos(0°)? —
1
8.
What is the value of tan(45°) * sin(90°)? —
1
9.
What is the value of (1 - sin²(theta)) / cos²(theta)? —
1
10.
What is the value of (sin(theta) + cos(theta))² - 2 sin(theta) cos(theta)? —
1
11.
If tan(theta) = 1, what is the value of (sin(theta) + cos(theta))²? —
2
12.
If cos(theta) = 1/√2, what is the value of tan(theta) for an acute angle theta? —
1
13.
What is the value of (sin(theta) / cosec(theta)) + (cos(theta) / sec(theta))? —
sin²(theta)
14.
What is the value of tan(60°) / sin(60°)? —
2
15.
What is the value of sin(30°) + tan(45°)? —
1.5
16.
What is the value of (sec(theta) * sin(theta)) / tan(theta)? —
1
17.
If cos(theta) = 1/2, what is the value of tan(theta) for an acute angle theta? —
√3
18.
If tan(theta) = 1/√3, what is the value of sin(theta) for an acute angle theta? —
1/2
19.
What is the value of sin(60°) * cos(30°)? —
3/4
20.
What is the value of sin(30°) * cos(60°)? —
1/4
21.
The angle of elevation of the top of a statue from a point on the ground 20 meters away from its base is 45°. What is the height of the statue? —
20 meters
22.
The angle of elevation of the sun is 60°. If a vertical pole casts a shadow of length 10 meters, what is the height of the pole? —
10√3 meters
23.
If tan(theta) = 5/12, what is the value of sec(theta) for an acute angle theta? —
13/12
24.
If cosec(theta) = 13/12, what is the value of cot(theta) for an acute angle theta? —
5/12
25.
The angle of elevation of the top of a pole from a point 30 meters away from its foot is 30°. What is the height of the pole? —
30/√3 meters
26.
What is the value of tan(60°) + cot(30°)? —
2√3
27.
The angle of elevation of the top of a tree from a point on the ground, which is 20 meters away from the foot of the tree, is 60°. What is the height of the tree? —
20√3 meters
28.
The angle of depression of an object on the ground from a point 50 meters high is 30°. What is the distance of the object from the point directly below the observer? —
50√3 meters
29.
If cos(theta) = 3/5, what is the value of (tan(theta) + sec(theta))? —
3
30.
If sin(theta) = 3/5 and theta is an acute angle, what is the value of tan(theta)? —
3/4
31.
If cosec(theta) = 5/3, what is the value of cot(theta) for an acute angle theta? —
4/3
32.
In a right-angled triangle, if the angle theta is such that sin(theta) = 3/5, what is the value of cos(theta)? —
4/5
33.
The angle of elevation of the top of a building from a point on the ground is 30°. If the distance from the point to the foot of the building is 30√3 meters, what is the height of the building? —
30 meters
34.
The angle of elevation of the top of a cliff from a boat is 30°. If the boat is 60√3 meters away from the cliff, what is the height of the cliff? —
60 meters
35.
If tan(theta) = 1, what is the value of theta in degrees? —
45°
36.
If sin(theta) = 1/2, what is the value of theta in degrees? —
30°
37.
If sin(theta) = cos(theta), what is the value of theta in degrees? —
45°
38.
A kite is flying at a height of 60 meters above the ground. The string attached to the kite makes an angle of 60° with the horizontal. What is the length of the string? —
40√3 meters
39.
In a right-angled triangle ABC, right-angled at B, if AC = 10 and angle A = 30°, what is the length of AB? —
5√3
40.
If sin(theta) = 5/13, what is the value of tan(theta) for an acute angle theta? —
5/12
41.
If sec(theta) = 13/12, what is the value of tan(theta) in a right-angled triangle where theta is acute? —
5/12
42.
In a right-angled triangle ABC, right-angled at B, if AB = 5 and BC = 12, what is the value of tan(C)? —
5/12
43.
The angle of elevation of the top of a tower from a point on the ground 100 meters away from its base is 30°. What is the height of the tower? —
100/√3 meters
44.
If the angle of elevation of a tower from a point 100 meters away from its base is 45°, what is the height of the tower? —
100 meters
45.
The angle of depression of a car from the top of a lighthouse 100 meters high is 60°. What is the distance of the car from the lighthouse? —
100/√3 meters
46.
The angle of elevation of the top of a building from a point on the ground 50 meters away from its base is 60°. What is the height of the building? —
50√3 meters
47.
In a right-angled triangle, if tan(theta) = 7/24, what is the value of sin(theta)? —
7/25
48.
In a right-angled triangle, the hypotenuse is 25 cm and one of the other sides is 7 cm. What is the sine of the angle opposite to the side of length 7 cm? —
7/25
49.
The angle of depression of a car from the top of a tower is 30°. If the height of the tower is 75 meters, how far is the car from the tower? —
75√3 meters
50.
If cos(theta) = 8/17, what is the value of sin(theta) for an acute angle theta? —
15/17