Height and Distance – General Questions

1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m
B. 200 m
C. 273 m
D. 300 m

Correct Answer: C. 273 m

Answer Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

the distance between the two ships is

2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?

A. 4√3 units
B. 8 units
C. 12 units
D. Data inadequate
E. None of these

Correct Answer: D. Data inadequate

Answer Explanation:

the distance between the base of the tower and the point P

3. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m

Correct Answer: D. 9.2 m

Answer Explanation:

The length of the ladder is

4. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

A. 21.6 m
B. 23.2 m
C. 24.72 m
D. None of these

Correct Answer: A. 21.6 m

Answer Explanation:

Let AB be the observer and CD be the tower.

The height of the tower is

5. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A. 149 m
B. 156 m
C. 173 m
D. 200 m

Correct Answer: C. 173 m

Answer Explanation:

Let AB be the tower.

the distance of point P from the foot of the tower is

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