From the top of a cliff,$60 \ m$ high,the angles of depression of the top and bottom of a tower are observed to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

The angle of elevation of a ladder leaning against a wall is $45^{\circ},$ and the foot of the ladder is $4.242 \ m$ away from the wall. The length of the ladder is (in $m$):

$A$ person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is $60^{\circ}$. When he moves $40 \ m$ away from the bank,he finds the angle of elevation to be $30^{\circ}$. The breadth of the river is (in $m$):

The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower 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

The upper part of a tree broken by the wind makes an angle of $30^{\circ}$ with the ground and the distance from the root to the point where the top of the tree touches the ground is $10 \ m$. What was the height of the tree?