Find the angle of elevation of the sun when the shadow of a pole $h$ meters high is $\sqrt{3} h$ meters long. (in $^{\circ}$)

Two ships are anchored in the opposite directions from a lighthouse. The angle of depression of one ship from the top of the lighthouse is $60^{\circ}$ and that of the other ship from the same place is found to be $30^{\circ}$. If the ship with the angle of depression of $60^{\circ}$ is $150\,m$ away from the lighthouse,find the distance between these two ships (in $m$).

The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.

From a point on the ground,the angle of elevation of the top of a tower is found to be $30^{\circ}$. Walking $30\, m$ towards the tower from that point,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the height of the tower (in $m$).

$A$ ladder leans against a wall such that its lower end makes an angle of measure $\theta$ with the ground. If its lower end is $a \ m$ away from the base of the wall,then the ladder reaches the wall at a height of $\ldots \ldots \ldots \ldots \ldots \ m$.

$A$ window of a house is $h$ meters above the ground. From the window,the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be $\alpha$ and $\beta$,respectively. Prove that the height of the other house is $h(1 + \tan \alpha \cot \beta)$ meters.