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?

$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)

The angle of elevation of the top of the tower from a point $x \, m$ away from the tower is $30^{\circ}$. Then the height of the tower is $\ldots \ldots \ldots \, m$.

$A$ ladder leans against a wall such that its lower end makes an angle of measure $\theta$ with the ground. If its lower end is $a \ m$ away from the base of the wall,then the ladder reaches the wall at a height of $\ldots \ldots \ldots \ldots \ldots \ m$.

From the top of a $70\, m$ tall tower,the angle of depression of the top and the base of a pole are found to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the pole from the tower and the height of the pole.

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.