Default Title

Question (41)

QN0036911

41. A tree breaks so that its top touches the ground 12 m from its foot. The broken part makes an angle of 60° with the ground. The length of the broken part is:

(A) 6 m
(B) 12 m
(C) 24 m
(D) 12√3 m

Correct Answer: C

Explanation:

If broken part is L, then L cos 60° = 12. Thus L = 24 m.

Link:

Report Error

Question (42)

QN0036912

42. For the tree in Question 41, the height of the remaining vertical part is:

(A) 6√3 m
(B) 12√3 m
(C) 24 m
(D) 6 m

Correct Answer: B

Explanation:

Remaining height = L sin 60° = 24 × √3/2 = 12√3 m.

Link:

Report Error

Question (43)

QN0036913

43. A slide is 2 m high and makes an angle of 30° with the ground. The length of the slide is:

(A) 2 m
(B) 4 m
(C) 2√3 m
(D) √3 m

Correct Answer: B

Explanation:

sin 30° = 2/L, so L = 4 m.

Link:

Report Error

Question (44)

QN0036914

44. A slide is 6 m long and makes an angle of 60° with the ground. Its vertical height is:

(A) 3 m
(B) 3√3 m
(C) 6√3 m
(D) 6 m

Correct Answer: B

Explanation:

Height = 6 sin 60° = 3√3 m.

Link:

Report Error

Question (45)

QN0036915

45. A tower is observed from the top of a 10 m high building. The angles of elevation of the tower top from two suitable observation points differ such that the resulting height calculation gives tan 60° and tan 45°. The additional height of the tower above the building is:

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

Correct Answer: A

Explanation:

The additional height corresponding to the difference between tan 60° and tan 45° is 10(√3 − 1) m.

Link:

Report Error

Question (46)

QN0036916

46. A lighthouse is 60 m high. The angle of depression of a ship from its top is 30°. The horizontal distance of the ship from the lighthouse is:

(A) 60 m
(B) 60√3 m
(C) 30√3 m
(D) 120 m

Correct Answer: B

Explanation:

tan 30° = 60/d, so d = 60√3 m.

Link:

Report Error

Question (47)

QN0036917

47. A lighthouse is 60 m high. The angles of depression of two ships on the same side are 30° and 60°. The distance between the ships is:

(A) 20√3 m
(B) 40√3 m
(C) 60√3 m
(D) 80√3 m

Correct Answer: B

Explanation:

Distances are 60√3 m and 60/√3 = 20√3 m. Difference = 40√3 m.

Link:

Report Error

Question (48)

QN0036918

48. A 30 m high tower is observed from a car at an angle of depression of 45°. When the car moves closer, the angle becomes 60°. The distance travelled by the car is:

(A) 30/√3 m
(B) 30(1 − 1/√3) m
(C) 30(√3 − 1) m
(D) 30 m

Correct Answer: B

Explanation:

Initial distance = 30 m and final distance = 30/√3 m. Distance travelled = 30 − 30/√3 = 30(1 − 1/√3) m.

Link:

Report Error

Question (49)

QN0036919

49. A tower is observed from a point at an angle of elevation of 45°. When the observer moves 10 m away, the angle becomes 30°. The height of the tower is:

(A) 5(√3 + 1) m
(B) 10√3 m
(C) 5(√3 − 1) m
(D) 10 m

Correct Answer: A

Explanation:

Let the original distance be x. Then h = x and h = (x + 10)/√3. Hence x√3 = x + 10, giving h = 5(√3 + 1) m.

Link:

Report Error

Question (50)

QN0036920

50. 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 m
(C) 10(√3 − 1) m
(D) 20 m

Correct Answer: A

Explanation:

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

Link:

Report Error

Question (41)

41. A tree breaks so that its top touches the ground 12 m from its foot. The broken part makes an angle of 60° with the ground. The length of the broken part is:

Explanation:

Link:

Question (42)

42. For the tree in Question 41, the height of the remaining vertical part is:

Explanation:

Link:

Question (43)

43. A slide is 2 m high and makes an angle of 30° with the ground. The length of the slide is:

Explanation:

Link:

Question (44)

44. A slide is 6 m long and makes an angle of 60° with the ground. Its vertical height is:

Explanation:

Link:

Question (45)

45. A tower is observed from the top of a 10 m high building. The angles of elevation of the tower top from two suitable observation points differ such that the resulting height calculation gives tan 60° and tan 45°. The additional height of the tower above the building is:

Explanation:

Link:

Question (46)

46. A lighthouse is 60 m high. The angle of depression of a ship from its top is 30°. The horizontal distance of the ship from the lighthouse is:

Explanation:

Link:

Question (47)

47. A lighthouse is 60 m high. The angles of depression of two ships on the same side are 30° and 60°. The distance between the ships is:

Explanation:

Link:

Question (48)

48. A 30 m high tower is observed from a car at an angle of depression of 45°. When the car moves closer, the angle becomes 60°. The distance travelled by the car is:

Explanation:

Link:

Question (49)

49. A tower is observed from a point at an angle of elevation of 45°. When the observer moves 10 m away, the angle becomes 30°. The height of the tower is:

Explanation:

Link:

Question (50)

50. 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:

Link:

Excel With Tutors

ExcelWithTutors

For Student

For Tutors

Learn

OUR POLICY