The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

From the top of a lighthouse $30 \ m$ high with its base at sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

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

If the angle of depression of a point $A$ on the ground from the top of a tower is $30^\circ$,then the angle of elevation of the top of the tower from the point $A$ will be .............. $^\circ $.

The angle of elevation of the sun,when the shadow of the pole is $\sqrt{3}$ times the height of the pole,is ....$^o$

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$, then $(\tan \alpha, \tan \beta)$ is equal to