Heights and Distances mcqs test 1

1. The angle of elevation of the sun, when the length of the shadow of a tree is 3 times the height of
the tree, is;

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

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:

4. An observer 1.6 m tall is 20 V3 m 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:

5. Two ships are sailing the sea on the two sides of a lighthouse, The angles of elevation of the top of
the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100 mn
high, the distance between the two ships is:

6. 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
elevation becomes 60°. What is the distance between the base of the tower and the point P?

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

8. A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an
angle of depression of 45° with the man’s eye when at a distance of 60 meters from the tower. After 5
seconds, the angle of depression becomes 30. What is the approximate speed of the boat, assuming
that it is running in still water?

9. On the same side of a 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
are ?

10. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming 9
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?

11. The top of a 15 meter high tower makes an angle of elevation of 60 with the bottom of an electric
POTE and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?