The angles of depression from the top of a lighthouse to two boats,which are $60 \, m$ apart and in the same direction (due east),are $45^{\circ}$ and $30^{\circ}$. The height of the lighthouse is:

The shadow of a tower standing on a level plane is found to be $50 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower. (In $m$)

From the top of a $25 \ m$ high cliff,the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower in $m$.

The angle of elevation of the sun,when the length of the shadow of a tree is $\sqrt{3}$ times the height of the tree,is (in $^{\circ}$)

On the level ground,the angle of elevation of the top of the tower is $30^{\circ}$. On moving $20 \ m$ nearer,the angle of elevation is $60^{\circ}$. The height of the tower is (in $m$):

$A$ man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of $45^{\circ}$ with the man's eye when at a distance of $60 \ m$ from the tower. After $5 \ s$,the angle of depression becomes $30^{\circ}$. What is the approximate speed (in $km/hr$) of the boat,assuming that it is running in still water?