The angle of elevation of the top of a tower from a point $20 \ m$ away from its base is $45^\circ$. The height of the tower is ....... $m$.

$A$ ladder $5 \ m$ long leans against a vertical wall. The bottom of the ladder is $3 \ m$ from the wall. If the bottom of the ladder is pulled $1 \ m$ farther from the wall,how much does the top of the ladder slide down the wall?

From the bottom of a pole of height $h,$ the angle of elevation of the top of a tower is $\alpha$ and the pole subtends an angle $\beta$ at the top of the tower. The height of the tower is

The shadow of a tower standing on a level plane is found to be $100 \ m$ longer when the sun's angle of elevation is $30^{\circ}$ than when it is $45^{\circ}$. 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

$A$ man is observing,from the top of a tower,a boat speeding towards the tower from a certain point $A$,with uniform speed. At that point,the angle of depression of the boat from the man's eye is $30^{\circ}$ (ignore the man's height). After sailing for $20 \text{ seconds}$ towards the base of the tower (which is at the level of water),the boat reaches a point $B$,where the angle of depression is $45^{\circ}$. Then,the time taken (in seconds) by the boat from $B$ to reach the base of the tower is: