Height and Distance MCQs

From the top and bottom of a straight hill; the angle of depression and elevation of the top of a pillar of 10 m height are observed to be 60° and 30° respectively. The height (in metres) of the hill is

The length of the shadow of a vertical tower on level ground increased by 10 m when the altitude of the sum changes from 45° to 30°. The height of the tower is:

The respective ratio between the height of tower and the point at some distance from its foot is 57 : 19√3. What is the angle (in degrees) of elevation of the top of the tower?

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 meter from point P observes that angle of elevation of the balloon is 60°. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15°. What is the length (in metres) of the ladder?

Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45° respectively. The ratio of the heights of A and B is:

From the top of 75 m high tower, the angle of depression of two points P and Q on opposite side of the base of the tower on level ground is $$\theta $$ and $$\phi $$, such that $$\tan \theta = \frac{3}{4}$$ and $$\tan \phi = \frac{5}{8}.$$ What is the distance between the points P and Q?

A ladder leaning against a wall makes an angle $$\theta $$ with the horizontal ground such that $$\tan \theta = \frac{{12}}{5}.$$ If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the food the ladder from the wall?

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).