$A$ 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 $^{\circ}$)?

Two towers of equal height stand on either side of a wide road which is $100 \, m$ wide. At a point on the road between the towers, the angles of elevation of the tops of the towers are $60^{\circ}$ and $30^{\circ}$. Find their heights in metres. (in $\sqrt{3}$)

The angles of depression from the top of a lighthouse to two boats,which are $60 \, m$ apart and in the same direction (due east),are $45^{\circ}$ and $30^{\circ}$. The height of the lighthouse is:

$A$ man having height $169 \; cm$ is standing near a pole. He casts a shadow $130 \; cm$ long. What is the length (in $cm$) of the pole if it casts a shadow $420 \; cm$ long?

$A$ tower subtends an angle of $30^{\circ}$ at a point on the same level as the foot of the tower. At a second point,$h \ m$ above the first,the angle of depression of the foot of the tower is $60^{\circ}$. The horizontal distance of the tower from the point 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: