Height And Distance - Aptitude MCQ Questions and Solutions with Explanations

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

E. None of these

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

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3.
The angle of elevation of a ladder leaning against a wall is 60º 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

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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 30º. The heights of the tower is:

A. 21.6 m

B. 23.2 m

C. 24.72 m

D. None of these

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5.
From a point P on a level ground, the angle of elevation of the top tower is 30º. 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

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6.
The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

A. 30º

B. 45º

C. 60º

D. 90º

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7.
The angle of elevation of the top of a tower from a certain point is 30°. If the observed moves 20 m towards the tower, the angle of elevation the angle of elevation of top of the tower increases by 15°. The height of the tower is

A. 17.3 m

B. 21.9 m

C. 27.3 m

D. 30 m

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8.
On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is-

A. 63.5 m

B. 76.9 m

C. 86.7 m

D. 90 m

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9.
The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-

A. \[35\sqrt 3 {\text{ m}}\]

B. \[70\sqrt 3 {\text{ m}}\]

C. \[\frac{{70\sqrt 3 }}{3}{\text{ m}}\]

D. \[{\text{70 m}}\]

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10.
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower ?

A. 14 min. 35 sec.

B. 15 min. 49 sec.

C. 16 min. 23 sec.

D. 18 min. 5 sec.

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Height And Distance - Aptitude MCQ Questions and Solutions with Explanations

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:

Answer & Solution

Answer & Solution

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

Answer & Solution

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 30º. The heights of the tower is:

Answer & Solution

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

Answer & Solution

6. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

Answer & Solution

7. The angle of elevation of the top of a tower from a certain point is 30°. If the observed moves 20 m towards the tower, the angle of elevation the angle of elevation of top of the tower increases by 15°. The height of the tower is

Answer & Solution

8. On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is-

Answer & Solution

9. The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-

Answer & Solution

10. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower ?

Answer & Solution

Read More Section(Height and Distance)

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:

3.
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. 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 30º. The heights of the tower is:

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

6.
The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

7.
The angle of elevation of the top of a tower from a certain point is 30°. If the observed moves 20 m towards the tower, the angle of elevation the angle of elevation of top of the tower increases by 15°. The height of the tower is

8.
On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is-

9.
The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is-

10.
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower ?