$A$ ladder leans on a wall to reach the height of $3\, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........$m.$

The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$. From another point $10 \, m$ vertically above the first,its angle of elevation is $45^{\circ}$. Find the height of the tower.

Find the angle of elevation of the sun when the shadow of a pole $h$ meters high is $\sqrt{3} h$ meters long. (in $^{\circ}$)

Watching from the top of a building $40 \, m$ high,the angle of depression of a moving car increases from $30^{\circ}$ to $45^{\circ}$ in some interval of time. Find the distance covered by the car in that interval of time. (in $m$)

The angle of elevation of the top of a vertical pole as observed from a point $20\, m$ away from the base of the pole is $60^\circ$. Find the height of the pole. (in $m$)

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $m \angle C = \theta$,then $\tan \theta = \dots$