From a point on the level ground, the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole, the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

An observer in a boat finds that the angle of elevation of the top of a tower standing on the top of a cliff is $60^\circ$ and that of the top of the cliff is $30^\circ$. If the height of the tower is $60 \ m$,then the height of the cliff is ... $m$.

The shadow of a tower of height $(1 + \sqrt{3}) \text{ m}$ standing on the ground is found to be $2 \text{ m}$ longer when the sun's elevation is $30^{\circ}$ than when the sun's elevation was $...^{\circ}$.

For a man,the angle of elevation of the highest point of the temple situated east of him is $60^\circ$. On walking $240 \ m$ to the north,the angle of elevation is reduced to $30^\circ$. The height of the temple is:

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

$A$ vertical pole (more than $100 \, ft$ high) consists of two portions,the lower being one-third of the whole. If the upper portion subtends an angle $\tan^{-1}(\frac{1}{2})$ at a point in a horizontal plane through the foot of the pole and at a distance of $40 \, ft$ from it,then the height of the pole is......$ft$.