The angle of elevation of a tower from a distance of $100 \ m$ from its foot is $30^{\circ}$. Then the height of the tower is (in $m$):

Two poles of height $7 \ m$ and $12 \ m$ stand on a plane ground. If the distance between their feet is $12 \ m$,the distance between their tops will be (in $m$):

$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

$A$ man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes $12$ minutes for the angle of depression to change from $30^{\circ}$ to $45^{\circ},$ how soon after this will the car reach the observation tower?

Two towers are situated on opposite banks of a river. One tower is $60 \ m$ high. From the top of this tower,the angles of depression of the top and the bottom of the other tower are $30^{\circ}$ and $60^{\circ}$ respectively. Find the width of the river and the height of the other tower (in $m$).

The angle of elevation of the top of a hill from each of the vertices $A, B, C$ of a horizontal triangle is $\alpha$. The height of the hill is