$A$ tower is $30 \ m$ high. An observer from the top of the tower makes an angle of depression of $60^{\circ}$ at the base of the building and an angle of depression of $45^{\circ}$ at the top of the building. What is the height of the building in metres?

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 $m$):

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

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 $^{\circ}$)

$A$ kite is flying at a height of $75 \ m$ from the ground. The string makes an angle $\Theta$ (where $\cot \Theta = 8/15$) with the level ground. Assuming that there is no slack in the string,the length of the string is equal to (in $m$):

When the sun is $30^{\circ}$ above the horizontal,the length (in $m$) of the shadow cast by a building $50 \ m$ high is