Observing from the top of a $150\, m$ high tower,the angle of depression of a cycle on the ground is found to be $60^{\circ}$. How far away is the cycle from the tower?

In a right triangle,if the measure of one of the angles is $30^{\circ}$,then the side opposite to the angle with measure $30^{\circ}$ is .......... times the hypotenuse.

During a storm,a $21 \,m$ high tree breaks but the broken part remains attached to the trunk and makes an angle of $30^{\circ}$ with the ground. At what height from the ground is the tree broken? (in $m$)

The angle of elevation of a cloud from a point $h$ metres above the surface of a lake is $\theta$ and the angle of depression of its reflection in the lake is $\phi$. Prove that the height of the cloud above the lake is $h\left(\frac{\tan \phi+\tan \theta}{\tan \phi-\tan \theta}\right).$

The height of a lighthouse is $100\, m$. Two boats are anchored in the opposite directions from the lighthouse. The angle of depression of each boat from the top of the lighthouse is found to be $30^\circ$. Find the distance between these two boats (in $m$).

As observed from the top of a tower $30 \, m$ high,the angle of depression of a stone on the ground is found to be $45^{\circ}$. Find the distance between the stone and the tower (in $m$).