The length of the shadow of a tower is $9 \text{ m}$ when the sun's altitude is $30^{\circ}$. What is the height of the tower? (In $m$)

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 $m$)

$A$ tower standing on a horizontal plane subtends a certain angle at a point $160 \; m$ apart from the foot of the tower. On advancing $100 \; m$ towards it,the tower is found to subtend an angle twice as before. The height of the tower is (in $m$):

The angle of elevation of the top of a hill from each of the vertices $A, B, C$ of a horizontal triangle is $\alpha$. The height of the hill is

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?

The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower is