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.