At a point,$15 \, m$ away from the base of a $15 \, m$ high house,the angle of elevation of the top is (in $^{\circ}$)

Two towers are situated on opposite banks of a river. One tower is $60 \ m$ high. From the top of this tower,the angles of depression of the top and the bottom of the other tower are $30^{\circ}$ and $60^{\circ}$ respectively. Find the width of the river and the height of the other tower (in $m$).

An observer on the top of a cliff,$200 \, m$ above the sea level,observes the angle of depression of two ships at anchor to be $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance (in $m$) between the ships if the line joining them stretches to the base of the cliff.

The angle of elevation of an aeroplane as observed from a point $30 \ m$ above the transparent water surface of a lake is $30^{\circ}$ and the angle of depression of the image of the aeroplane in the water of the lake is $60^{\circ}$. The height of the aeroplane from the water surface of the lake is (in $m$):

The angle of elevation of the top of a $TV$ tower from three points $A, B, C$ in a straight line through the foot of the tower are $\alpha, 2 \alpha, 3 \alpha$ respectively. If $AB = a$,the height of the tower is

In a rectangle,if the angle between a diagonal and a side is $30^{\circ}$ and the length of the diagonal is $6 \text{ cm}$,the area (in $\text{cm}^2$) of the rectangle is: