$A$ $10 \ m$ long ladder is placed against a wall. It is inclined at an angle of $30^{\circ}$ to the ground. The distance (in $m$) of the foot of the ladder from the wall is (Given $\sqrt{3} = 1.732$)

$A$ kite is flying at a height of $75 \ m$ from the ground. The string makes an angle $\Theta$ (where $\cot \Theta = 8/15$) with the level ground. Assuming that there is no slack in the string,the length of the string is equal to (in $m$):

The angle of elevation of an aeroplane as observed from a point $30 \ m$ above the transparent water surface of a lake is $30^{\circ}$ and the angle of depression of the image of the aeroplane in the water of the lake is $60^{\circ}$. The height of the aeroplane from the water surface of the lake 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?

The angle of elevation of a tower from a distance of $100 \ m$ from its foot is $30^{\circ}$. Then the height of the tower is (in $m$):

$A$ 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?