The angle of elevation of a ladder leaning against a house is $60^{\circ}$ and the foot of the ladder is $6.5 \ m$ from the house. Find the length of the ladder in metres.

On the level ground,the angle of elevation of the top of the tower is $30^{\circ}$. On moving $20 \ m$ nearer,the angle of elevation is $60^{\circ}$. The height of the tower is (in $m$):

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^{\circ}$. After some time,the angle of depression becomes $60^{\circ}$. The distance (in $m$) travelled by the car during this time is

The angle of elevation of the top of an unfinished tower at a point distant $120 \ m$ from its base is $45^{\circ}$. If the elevation of the top at the same point is to be $60^{\circ}$,the tower must be raised to a height of:

$A$ tower subtends an angle of $30^{\circ}$ at a point on the same level as the foot of the tower. At a second point,$h \ m$ above the first,the angle of depression of the foot of the tower is $60^{\circ}$. The horizontal distance of the tower from the point is

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 $^{\circ}$)