Exercise

If the angle of elevation of a cloud from a point $200 \mathrm{m}$ above a lake is $30°$ and the angle of depression of its reflection in the lake is $60°$, then the height of the cloud above the lake is

A tower stands at the centre of a circular park. $\mathrm{A}$ and $\mathrm{B}$ are two points on the boundary of the park such that $\mathrm{AB} (=a)$ subtends an angle of $60°$ at the foot of the tower, and the angle of elevation of the top of the tower from $\mathrm{A}$ or $\mathrm{B}$ is $30°$. The height of the tower is

The upper part of a tree broken over by the wind makes an angle of $30°$ with the ground and the distance from the root to the point where the top of the tree touches the ground is $10 \mathrm{m}$. Then height of the tree is

An aeroplane flying at the height of $3000 \mathrm{m}$ above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are $60°$ and $45°$ respectively. Then the height of the lower plane from the ground is

A person standing on the bank of a river observes that the angle of the top of a tree on the opposite bank of the river is $60°$ and when he retires $40 \mathrm{metres}$ away from the tree the angle of elevation becomes $30°$. The breadth of the river is

If the angles of elevation of a tower from two points distant $a$ and $b$ ($a>b$) from its foot and in the same straight line from it are $30°$ and $60°$, then the height of the tower is

A tower shadows an angle of $30°$ at point on the same level as its foot. At a second point $h \mathrm{metres}$ above the first, the depression of the foot of the tower is $60°$. The height of the tower is

In a rectangle, the angle between a diagonal and a pole is $30°$ and the length of its diagonal is $8 \mathrm{cm}$. Then the area of the rectangle is