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

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 $m$):

$A$ tower is $30 \ m$ high. An observer from the top of the tower makes an angle of depression of $60^{\circ}$ at the base of the building and an angle of depression of $45^{\circ}$ at the top of the building. What is the height of the building in metres?

When the sun is $30^{\circ}$ above the horizontal,the length (in $m$) of the shadow cast by a building $50 \ m$ high 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:

$A$ person of height $6 \ ft$ wants to pluck a fruit which is on a $\frac{26}{3} \ ft$ high tree. If the person is standing $\frac{8}{\sqrt{3}} \ ft$ away from the base of the tree,then at what angle should he throw a stone so that it hits the fruit (in $^{\circ}$)?