$A$ ladder $15 \, m$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall,find the height of the wall in $m$.

$A$ pole stands erect on the ground. $A$ wire tied to the top of the pole is affixed at a point on the ground. If the length of the wire is $7 \, m$ and the wire makes an angle of $30^{\circ}$ with the ground,find the height of the pole (in $m$).

In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 16$ and $BC = 8$,then $m \angle C = \dots$ (in $^{\circ}$)

Two ships are anchored in the opposite directions from a lighthouse. The angle of depression of one ship from the top of the lighthouse is $60^{\circ}$ and that of the other ship from the same place is found to be $30^{\circ}$. If the ship with the angle of depression of $60^{\circ}$ is $150\,m$ away from the lighthouse,find the distance between these two ships (in $m$).

From the top of a tower,the angles of depression of two vehicles on the same side of the tower are found to be $\alpha$ and $\beta$ $(\alpha > \beta)$. If the distance between the vehicles is $b$,show that the height of the tower is $\frac{b \tan \alpha \tan \beta}{\tan \alpha - \tan \beta}$.

$A$ cable tied to the top of an electric pole is affixed at a point on the ground $a \text{ m}$ away from the pole. If the cable makes an angle $\theta$ with the ground,then prove that the height of the pole is $a \tan \theta \text{ m}$ and the length of the wire is $a \sec \theta \text{ m}$.