Q.1 A boy is standing 30 m away from a building. The angle of elevation of the top of the building is 45°. Find the height of the building.
15 m
30 m
45 m
60 m
Explanation - tan 45° = height / distance ⇒ 1 = h / 30 ⇒ h = 30 m.
Correct answer is: 30 m
Q.2 From the top of a 20 m high building, the angle of depression of a car on the ground is 30°. Find the distance of the car from the building.
10√3 m
20√3 m
30√3 m
40√3 m
Explanation - tan 30° = 20 / d ⇒ 1/√3 = 20 / d ⇒ d = 20√3 m.
Correct answer is: 20√3 m
Q.3 A ladder 10 m long is leaning against a wall. The foot of the ladder is 6 m away from the wall. Find the height of the wall.
6 m
8 m
10 m
12 m
Explanation - By Pythagoras: height = √(10² - 6²) = √64 = 8 m.
Correct answer is: 8 m
Q.4 The angle of elevation of the top of a tower from a point on the ground is 60°. If the point is 50 m away from the foot of the tower, find the height of the tower.
50 m
50√3 m
100 m
100√3 m
Explanation - tan 60° = h / 50 ⇒ √3 = h / 50 ⇒ h = 50√3.
Correct answer is: 50√3 m
Q.5 The top of a tree is observed from a point 60 m from its base at an angle of elevation of 30°. Find the height of the tree.
20√3 m
30 m
30√3 m
60 m
Explanation - tan 30° = h / 60 ⇒ 1/√3 = h / 60 ⇒ h = 20√3.
Correct answer is: 20√3 m
Q.6 The angle of elevation of the top of a building from a point on the ground is 45°. If the point is 40 m away, find the height of the building.
20 m
30 m
40 m
50 m
Explanation - tan 45° = h / 40 ⇒ h = 40 m.
Correct answer is: 40 m
Q.7 The angle of depression from the top of a tower 100 m high to a car is 30°. Find the distance of the car from the base of the tower.
100/√3 m
100√3 m
200 m
50√3 m
Explanation - tan 30° = 100 / d ⇒ 1/√3 = 100 / d ⇒ d = 100√3 m.
Correct answer is: 100√3 m
Q.8 A person standing on the bank of a river observes the top of a tree on the opposite bank at an elevation of 60°. If the height of the tree is 30√3 m, find the width of the river.
10 m
20 m
30 m
40 m
Explanation - tan 60° = 30√3 / width ⇒ √3 = 30√3 / width ⇒ width = 30 m.
Correct answer is: 30 m
Q.9 The shadow of a vertical pole is equal to its height. Find the angle of elevation of the sun.
30°
45°
60°
90°
Explanation - tan θ = h / h = 1 ⇒ θ = 45°.
Correct answer is: 45°
Q.10 A man 1.7 m tall observes the top of a tower at an angle of elevation of 60°. If he is standing 20 m away from the foot of the tower, find the height of the tower.
31.34 m
34.5 m
36.34 m
37.7 m
Explanation - tan 60° = (h - 1.7) / 20 ⇒ √3 = (h - 1.7)/20 ⇒ h = 36.34 m.
Correct answer is: 36.34 m
Q.11 From a point on the ground, the angles of elevation of the top and bottom of a flag on a pole are 60° and 30° respectively. If the flag is 10 m long, find the height of the pole.
15 m
20 m
25 m
30 m
Explanation - Using tan 60° and tan 30° with same base, solving gives total pole height = 25 m.
Correct answer is: 25 m
Q.12 The angle of elevation of the top of a tower from two points A and B on level ground on the same line and in opposite directions are 30° and 45° respectively. If AB = 40 m, find the height of the tower.
20 m
30 m
40 m
50 m
Explanation - By applying tan 30° and tan 45° on two triangles and solving, h = 20 m.
Correct answer is: 20 m
Q.13 If the shadow of a tower is 5 m longer when the sun’s altitude is 45° than when it is 60°, find the height of the tower.
5 m
10 m
15 m
20 m
Explanation - tan 45° = h / (x + 5), tan 60° = h / x ⇒ solving gives h = 10 m.
Correct answer is: 10 m
Q.14 A balloon is 60 m above the ground. The angle of elevation of the balloon from a point on the ground is 60°. Find the distance of the point from the balloon’s foot on the ground.
20√3 m
30√3 m
60√3 m
120 m
Explanation - tan 60° = 60 / d ⇒ √3 = 60 / d ⇒ d = 20√3.
Correct answer is: 20√3 m
Q.15 The angle of elevation of a cloud from a point h meters above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud above the lake.
√3h
2√3h
3√3h
4√3h
Explanation - Using tan 30° and tan 60° relations for actual and reflection heights gives 2√3h.
Correct answer is: 2√3h
Q.16 A tower 50 m high casts a shadow of length 50√3 m. Find the angle of elevation of the sun.
30°
45°
60°
75°
Explanation - tan θ = 50 / (50√3) = 1/√3 ⇒ θ = 30°.
Correct answer is: 30°
Q.17 The angle of elevation of the top of a building is observed to be 30° from the ground at a distance of 40 m. Find the height of the building.
20 m
40 m
40√3 m
20√3 m
Explanation - tan 30° = h / 40 ⇒ h = 40 / √3 = 20√3.
Correct answer is: 20√3 m
Q.18 A man on a ship observes the top of a lighthouse at an elevation of 45°. If the ship is 200 m from the lighthouse, find the height of the lighthouse.
100 m
150 m
200 m
250 m
Explanation - tan 45° = h / 200 ⇒ h = 200 m.
Correct answer is: 200 m
Q.19 The angles of elevation of the top of a tower from two points at a distance 4 m and 9 m from its foot and in the same straight line with it are complementary. Find the height of the tower.
5 m
6 m
7 m
8 m
Explanation - Let angle = θ and (90°-θ). Then h/4 = tan θ, h/9 = cot θ ⇒ solving gives h = 6 m.
Correct answer is: 6 m
Q.20 From the top of a hill, the angles of depression of two consecutive kilometer stones due east are 30° and 45°. Find the height of the hill.
500 m
1000 m
1500 m
2000 m
Explanation - tan 30° = h/d1, tan 45° = h/d2, d1-d2=1000 ⇒ solving gives h = 500 m.
Correct answer is: 500 m
Q.21 The angle of elevation of the top of a vertical tower is 30°. On walking 100 m towards it, the angle becomes 60°. Find the height of the tower.
25√3 m
50√3 m
75√3 m
100√3 m
Explanation - Let initial distance = x. tan 30° = h/x, tan 60° = h/(x-100). Solving gives h = 50√3 m.
Correct answer is: 50√3 m
Q.22 A tower subtends an angle of 60° at a point on the ground. If the height of the tower is 20√3 m, find the distance of the tower from the point.
10 m
20 m
30 m
40 m
Explanation - tan 60° = (20√3)/d ⇒ √3 = (20√3)/d ⇒ d = 20 m.
Correct answer is: 20 m
Q.23 Two poles of equal heights are standing opposite each other on either side of a road 80 m wide. From a point between them, the angles of elevation of their tops are 60° and 30°. Find the height of the poles.
20√3 m
30√3 m
40√3 m
60√3 m
Explanation - Let distances be x and (80-x). tan 60° = h/x, tan 30° = h/(80-x). Solving gives h = 20√3.
Correct answer is: 20√3 m
Q.24 The angle of elevation of the top of a tree from a point 50 m away is 30°. Find the height of the tree.
25 m
25√3 m
50 m
50√3 m
Explanation - tan 30° = h / 50 ⇒ 1/√3 = h / 50 ⇒ h = 25√3.
Correct answer is: 25√3 m