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

The shadow of a tower standing on a level ground is found to be $40 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the length of the tower. (In $m$)

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 $m$)

$A$ person walking along a straight road towards a hill observes at two points,separated by a distance of $\sqrt{3} \text{ km}$,that the angles of elevation of the hill are $30^{\circ}$ and $60^{\circ}$. 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?

In a rectangle,if the angle between a diagonal and a side is $30^{\circ}$ and the length of the diagonal is $6 \text{ cm}$,the area (in $\text{cm}^2$) of the rectangle is: