An observer $1.5\, m$ tall is $28.5\, m$ away from a tower. The angle of elevation of the top of the tower from his eyes is $45^\circ$. Then the height of the tower is ............ $m$.

The angle of elevation of the top of tower $N$ from the base of tower $M$ is $40^{\circ}$. The angle of elevation of the top of tower $M$ from the base of tower $N$ is $55^{\circ}$. Then,.......

$A$ cable tied to the top of an electric pole is affixed at a point on the ground $a \text{ m}$ away from the pole. If the cable makes an angle $\theta$ with the ground,then prove that the height of the pole is $a \tan \theta \text{ m}$ and the length of the wire is $a \sec \theta \text{ m}$.

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.

The angle of elevation of the top of the temple on the bank of the river from a point exactly opposite to the temple on the other bank of the river is $30^{\circ}$. If the height of the temple is $20 \ m$,then the breadth of the river is $\ldots \ldots \ldots \ldots \ m$.

$A$ ladder leans on a wall to reach a 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 ........... $m$.