The angle of elevation of a ladder leaning against a wall is $45^{\circ},$ and the foot of the ladder is $4.242 \ m$ away from the wall. The length of the ladder is (in $m$):

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

An aeroplane flying at a height of $5000 \; m$ from the ground passes vertically above another aeroplane at an instant. At that instant,the angles of elevation of the two aeroplanes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. The vertical distance between the aeroplanes at that instant is:

$A$ tower stands at the end of a straight road. The angles of elevation of the top of the tower from two points on the road $500 \ m$ apart are $45^{\circ}$ and $60^{\circ},$ respectively. Find the height of the tower.

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 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