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Question (21)

QN0036891

21. A 15 m high building is viewed from a point on the ground at an angle of elevation of 30°. The distance of the point from the building is:

(A) 5√3 m
(B) 15√3 m
(C) 30 m
(D) 15 m

Correct Answer: B

Explanation:

tan 30° = 15/d, so d = 15√3 m.

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Question (22)

QN0036892

22. A flagstaff is fixed on a 12 m high building. From a point on the ground, the angles of elevation of the top of the building and the top of the flagstaff are 45° and 60°, respectively. The height of the flagstaff is:

(A) 12(√3 − 1) m
(B) 12√3 m
(C) 12(√3 + 1) m
(D) 6(√3 − 1) m

Correct Answer: A

Explanation:

Distance = 12 m. Total height = 12√3 m. Flagstaff height = 12√3 − 12 = 12(√3 − 1) m.

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Question (23)

QN0036893

23. An 8 m flagstaff stands on a building. From a point on the ground, the angles of elevation of the top of the building and the top of the flagstaff are 30° and 45°, respectively. The height of the building is:

(A) 4(√3 + 1) m
(B) 4(√3 − 1) m
(C) 8√3 m
(D) 4√3 m

Correct Answer: A

Explanation:

If building height is h, then h tan 45°/tan 30° gives h = 8/(√3 − 1) = 4(√3 + 1) m.

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Question (24)

QN0036894

24. A tower is observed from a point 10 m away at an angle of elevation of 60°. The height of the tower is:

(A) 10 m
(B) 5√3 m
(C) 10√3 m
(D) 20 m

Correct Answer: C

Explanation:

Height = 10 tan 60° = 10√3 m.

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Question (25)

QN0036895

25. From a point on the ground, the angle of elevation of a tower is 30°. After moving 20 m towards the tower, the angle becomes 45°. The height of the tower is:

(A) 10(√3 + 1) m
(B) 20(√3 + 1) m
(C) 10√3 m
(D) 20 m

Correct Answer: A

Explanation:

Let the nearer distance be x. Then h = x and h = (x + 20)/√3. Thus x√3 = x + 20, giving h = 10(√3 + 1) m.

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Question (26)

QN0036896

26. A person observes the top of a tower at 30°. On moving 10 m closer, the angle becomes 60°. The height of the tower is:

(A) 5√3 m
(B) 10√3 m
(C) 5 m
(D) 15 m

Correct Answer: A

Explanation:

Let the nearer distance be x. Then h = x√3 and h = (x + 10)/√3. Solving gives x = 5/√3 and h = 5√3 m.

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Question (27)

QN0036897

27. From the top of an 18 m high building, the angle of depression of a point on the ground is 45°. The horizontal distance of the point from the building is:

(A) 9 m
(B) 18 m
(C) 18√3 m
(D) 36 m

Correct Answer: B

Explanation:

tan 45° = 18/d, so d = 18 m.

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Question (28)

QN0036898

28. From the top of a tower, the angle of depression of a point on the ground is 30°. If the horizontal distance is 20√3 m, the height of the tower is:

(A) 10 m
(B) 20 m
(C) 30 m
(D) 40 m

Correct Answer: B

Explanation:

Height = 20√3 tan 30° = 20 m.

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Question (29)

QN0036899

29. A building is 30 m high. The angle of depression of a point on the ground from its top is 60°. The horizontal distance of the point from the building is:

(A) 10√3 m
(B) 30√3 m
(C) 15√3 m
(D) 10 m

Correct Answer: A

Explanation:

tan 60° = 30/d, so d = 10√3 m.

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Question (30)

QN0036900

30. Two buildings are 30 m apart. From the top of the shorter building, the angle of elevation of the top of the taller building is 30°. The difference in their heights is:

(A) 10√3 m
(B) 15√3 m
(C) 30√3 m
(D) 10 m

Correct Answer: A

Explanation:

Height difference = 30 tan 30° = 10√3 m.

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Question (21)

21. A 15 m high building is viewed from a point on the ground at an angle of elevation of 30°. The distance of the point from the building is:

Explanation:

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Question (22)

22. A flagstaff is fixed on a 12 m high building. From a point on the ground, the angles of elevation of the top of the building and the top of the flagstaff are 45° and 60°, respectively. The height of the flagstaff is:

Explanation:

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Question (23)

23. An 8 m flagstaff stands on a building. From a point on the ground, the angles of elevation of the top of the building and the top of the flagstaff are 30° and 45°, respectively. The height of the building is:

Explanation:

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Question (24)

24. A tower is observed from a point 10 m away at an angle of elevation of 60°. The height of the tower is:

Explanation:

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Question (25)

25. From a point on the ground, the angle of elevation of a tower is 30°. After moving 20 m towards the tower, the angle becomes 45°. The height of the tower is:

Explanation:

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Question (26)

26. A person observes the top of a tower at 30°. On moving 10 m closer, the angle becomes 60°. The height of the tower is:

Explanation:

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Question (27)

27. From the top of an 18 m high building, the angle of depression of a point on the ground is 45°. The horizontal distance of the point from the building is:

Explanation:

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Question (28)

28. From the top of a tower, the angle of depression of a point on the ground is 30°. If the horizontal distance is 20√3 m, the height of the tower is:

Explanation:

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Question (29)

29. A building is 30 m high. The angle of depression of a point on the ground from its top is 60°. The horizontal distance of the point from the building is:

Explanation:

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Question (30)

30. Two buildings are 30 m apart. From the top of the shorter building, the angle of elevation of the top of the taller building is 30°. The difference in their heights is:

Explanation:

Link:

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