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Question (31)

QN0036901

31. A 30 m high tower is observed from the foot of another vertical building. If the angle of elevation of the tower top is 30°, the distance between the two buildings is:

(A) 30 m
(B) 30√3 m
(C) 15√3 m
(D) 60 m

Correct Answer: B

Explanation:

tan 30° = 30/d, hence d = 30√3 m.

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Question (32)

QN0036902

32. From the top of a 7 m high building, the angle of depression of the foot of a tower is 45°. The horizontal distance between the building and the tower is:

(A) 3.5 m
(B) 7 m
(C) 7√3 m
(D) 14 m

Correct Answer: B

Explanation:

tan 45° = 7/d, so d = 7 m.

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Question (33)

QN0036903

33. From the same point on the ground, the angles of elevation of the tops of a 20 m high building and a tower are 30° and 60°, respectively. The height of the tower is:

(A) 20 m
(B) 40 m
(C) 60 m
(D) 80 m

Correct Answer: C

Explanation:

Distance = 20/tan 30° = 20√3 m. Tower height = 20√3 tan 60° = 60 m.

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Question (34)

QN0036904

34. Two vertical poles stand on opposite sides of a 40 m wide road. A point on the road is 10 m from the first pole. If the angle of elevation of the first pole's top is 45°, its height is:

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

Correct Answer: A

Explanation:

Height = 10 tan 45° = 10 m.

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Question (35)

QN0036905

35. Two equal vertical poles are 50 m apart. A point between them is 20 m from the first pole. If the angle of elevation of the first pole's top is 30°, the height of each pole is:

(A) 20/√3 m
(B) 20√3 m
(C) 10√3 m
(D) 25 m

Correct Answer: A

Explanation:

Height = 20 tan 30° = 20/√3 m.

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Question (36)

QN0036906

36. A bridge is 4 m above the level of a river. The angles of depression of the two opposite banks from the bridge are 45° and 30°. The width of the river is:

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

Correct Answer: A

Explanation:

Distances are 4 cot 45° = 4 m and 4 cot 30° = 4√3 m. Width = 4 + 4√3 = 4(1 + √3) m.

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Question (37)

QN0036907

37. A bridge is 6 m above a river. The angles of depression of the two opposite banks are 30° and 60°. The width of the river is:

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

Correct Answer: A

Explanation:

Width = 6 cot 30° + 6 cot 60° = 6√3 + 6/√3 = 6(√3 + 1/√3) m.

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Question (38)

QN0036908

38. A balloon is 50 m above the ground. If its angle of elevation from a point on the ground is 30°, its horizontal distance from the point is:

(A) 50√3 m
(B) 25√3 m
(C) 50/√3 m
(D) 100 m

Correct Answer: A

Explanation:

tan 30° = 50/d, so d = 50√3 m.

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Question (39)

QN0036909

39. A balloon is at a height of 30√3 m. Its angle of elevation from a point changes from 60° to 30°. The horizontal distance through which the balloon moves away is:

(A) 20 m
(B) 30 m
(C) 60 m
(D) 90 m

Correct Answer: C

Explanation:

Initial distance = 30 m and final distance = 90 m. Therefore, distance moved = 60 m.

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Question (40)

QN0036910

40. A tower is observed at an angle of elevation of 30°. When the observer moves 40 m towards it, the angle becomes 60°. The height of the tower is:

(A) 20√3 m
(B) 40√3 m
(C) 20 m
(D) 40 m

Correct Answer: A

Explanation:

Let nearer distance be x. Then h = x√3 and h = (x + 40)/√3. Solving gives x = 20/√3 and h = 20√3 m.

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Question (31)

31. A 30 m high tower is observed from the foot of another vertical building. If the angle of elevation of the tower top is 30°, the distance between the two buildings is:

Explanation:

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Question (32)

32. From the top of a 7 m high building, the angle of depression of the foot of a tower is 45°. The horizontal distance between the building and the tower is:

Explanation:

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Question (33)

33. From the same point on the ground, the angles of elevation of the tops of a 20 m high building and a tower are 30° and 60°, respectively. The height of the tower is:

Explanation:

Link:

Question (34)

34. Two vertical poles stand on opposite sides of a 40 m wide road. A point on the road is 10 m from the first pole. If the angle of elevation of the first pole's top is 45°, its height is:

Explanation:

Link:

Question (35)

35. Two equal vertical poles are 50 m apart. A point between them is 20 m from the first pole. If the angle of elevation of the first pole's top is 30°, the height of each pole is:

Explanation:

Link:

Question (36)

36. A bridge is 4 m above the level of a river. The angles of depression of the two opposite banks from the bridge are 45° and 30°. The width of the river is:

Explanation:

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Question (37)

37. A bridge is 6 m above a river. The angles of depression of the two opposite banks are 30° and 60°. The width of the river is:

Explanation:

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Question (38)

38. A balloon is 50 m above the ground. If its angle of elevation from a point on the ground is 30°, its horizontal distance from the point is:

Explanation:

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Question (39)

39. A balloon is at a height of 30√3 m. Its angle of elevation from a point changes from 60° to 30°. The horizontal distance through which the balloon moves away is:

Explanation:

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Question (40)

40. A tower is observed at an angle of elevation of 30°. When the observer moves 40 m towards it, the angle becomes 60°. The height of the tower is:

Explanation:

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