The angle of elevation of the sun when the length of the shadow of a pole is equal to its height is

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

$A$ 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

From a point $20 \; m$ away from the foot of a tower,the angle of elevation of the top of the tower is $30^{\circ}$. The height of the tower is:

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

Two posts are $2 \text{ m}$ apart. Both posts are on the same side of a tree. If the angles of depression of these posts when observed from the top of the tree are $45^{\circ}$ and $60^{\circ}$ respectively,then the height of the tree is: