From the top of a lighthouse,$50 \ m$ above the sea,the angle of depression of an incoming boat is $30^{\circ}$. How far is the boat from the lighthouse?

If a flagstaff of $6 \, m$ height placed on the top of a tower throws a shadow of $2 \sqrt{3} \, m$ along the ground,then the angle that the sun makes with the ground is

$A$ man having height $169 \; cm$ is standing near a pole. He casts a shadow $130 \; cm$ long. What is the length (in $cm$) of the pole if it casts a shadow $420 \; cm$ long?

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 length of a shadow of a vertical tower is $\frac{1}{\sqrt{3}}$ times its height. The angle of elevation of the Sun is (in $^{\circ}$)

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