Height and Distance MCQs

When the sun's altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

From a point P on a level ground, the angle of elevation of the top tower is 30o. If the tower is 200 m high, the distance of point P from the foot of the tower is:

The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?

The angle of elevation of the top of the tower from a point on the ground is $${\sin ^{ - 1}}\left({\frac{3}{5}} \right).$$ If the point of observation is 20 meters away from the foot of the tower, what is the height of the tower?

A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall $$\left( {\sqrt 3 = 1.73} \right)$$

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 45o. What is the distance between the base of the tower and the point P?

A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?

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 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?

An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?