In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 20$ and $BC = 10$,then $m\angle ACB = \ldots$ (in $^{\circ}$)

From the top of a hill $100 \, m$ high,the angles of depression of the top and the bottom of a tower are observed to be $30^{\circ}$ and $45^{\circ}$ respectively. Find the height of the tower in meters.

$A$ 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 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.

The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.

$A$ 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 $\ldots \ldots \ldots \ldots \ldots \ m$.