Watching from the top of a tower,the angles of depression of two houses $A$ and $B$ are found to be $25^{\circ}$ and $40^{\circ}$ respectively. Then,.......

From a balloon vertically above a straight road,the angles of depression of two cars at an instant are found to be $45^{\circ}$ and $60^{\circ}$. If the cars are $100 \, m$ apart,find the height of the balloon.

$A$ pole stands vertically on the ground. The length of the shadow of the pole is $\frac{1}{\sqrt{3}}$ times the height of the pole. Then,the angle of elevation of the sun is $\ldots \ldots \ldots \ldots . . .$ (in $^\circ$)

Watching from the top of a $150\, m$ high tower,the angles of depression of two houses situated in the east and west of the tower are found to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the distance between the houses in meters.

Watching from a point on the ground $20 \, m$ away from the base of an erect pole,the angle of elevation of the top of the pole is found to be $45^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

$A$ contractor plans to install two slides for the children to play in a park. For the children below the age of $5$ years,she prefers to have a slide whose top is at a height of $1.5 \, m$,and is inclined at an angle of $30^{\circ}$ to the ground,whereas for elder children,she wants to have a steep slide at a height of $3 \, m$,and inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide in each case?