The angle of elevation of a point situated at a distance of $70 \ m$ from the base of a tower is $45^\circ$. The height of the tower is ..... $m$.

$A$ spherical gas balloon of radius $16 \ m$ subtends an angle $60^{\circ}$ at the eye of the observer $A$,while the angle of elevation of its center from the eye of $A$ is $75^{\circ}$. Then the height (in $m$) of the top most point of the balloon from the level of the observer's eye is:

If the angle of elevation of the top of a tower at a distance of $500 \, m$ from its foot is $30^\circ$,then the height of the tower is:

$A$ tower of height $b$ subtends an angle $\alpha$ at a point $O$ on the level of the foot of the tower and at a distance $a$ from the foot of the tower. If a pole of height $p$ mounted on the tower also subtends an equal angle $\alpha$ at $O$,the height of the pole $p$ is:

From the base of a pole of height $20 \text{ m}$,the angle of elevation of the top of a tower is $60^{\circ}$. The pole subtends an angle of $30^{\circ}$ at the top of the tower. Then the height of the tower is

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is