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 a point $P$ on a level ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the tower is $100 \ m$ high,the distance (in $m$) of point $P$ from the foot of the tower is:

The distance between two pillars is $120 \text{ m}$. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in $\text{m}$) of the taller pillar is (Use: $\sqrt{3} = 1.732$)

From the top of a lighthouse,$50 \ m$ above the sea,the angle of depression of an incoming boat is $30^{\circ}$. How far is the boat from the lighthouse?

From a point $P$ on the ground,the angle of elevation of the top of a $10 \ m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building,and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff. (Take $\sqrt{3} = 1.732$) (In $m$)

The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$. The angle of elevation of the sun is (in $^{\circ}$)