The angle of elevation of the top of a building from the foot of a tower is $30°$ and the angle of elevation of the top of the tower from the foot of the building is $60°$. If the building is $15$ m high, find the height of the tower.

Two towers are at a distance of $120$ meters from each other. The angle of depression from the top of the second tower to the top of the first tower is $30°$. If the second tower is $40$m high then find the height of the first tower.

If the angles of elevation of the top of the tower from two points at distances of $a$ and $b$ cm from the base of the tower and in the same straight line with it, are complementary, then show that the height of the tower is $\sqrt{ab}$.

The angle of elevation is $60°$ from the top of a $15 \mathrm{m}$ high building to the top of a tower and the angle of depression to the bottom of the tower is $30°$. Find the height of the tower and the distance between the tower and the building.

The distance between two points $\mathrm{A}$ and $\mathrm{B}$on the same side of a river bank is  $40 \mathrm{m}$. There is a point $\mathrm{C}$ on the opposite, parallel river bank such that $\angle \mathrm{BAC}=60°$ and $\angle \mathrm{ABC}=30°$.Find the width of the river.

The angles of depression on a point $\mathrm{P}$ on the ground made by the peak of a temple and the flag on top of it are $30°$ and $60°$ respectively. If the temple is $10 \mathrm{m}$ high, find the height of the flag.

Two electricity poles of equal height are on the opposite sides of a $40 \mathrm{m}$ wide road. The angles of depression formed by the two poles at a point on the road are $30°$ and $60°$ respectively. Find the height of the poles and their respective distance from the point.

An observer spots a balloon moving at a height of $90 \mathrm{m}$ above the horizon. If at a certain time the angle of elevation made by the balloon with the observer’s eyes is $45°$ which reduces to $30°$ after some time then find the distance covered by the balloon.