Watching from the top of a building and from a window $10 \, m$ below the top,the angles of depression of a car on the ground are found to be $60^{\circ}$ and $45^{\circ}$ respectively. Find the distance of the car from the building. (in $m$)

$A$ tree stands vertically on the bank of a river. The angle of elevation of the top of the tree from a point exactly opposite to the tree on the other bank of the river is $60^{\circ}$. The angle of elevation of the top of the tree from a point $40 \ m$ away from that point is $30^{\circ}$. Find the width of the river and the height of the tree.

An observer $1.5\, m$ tall is $28.5\, m$ away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney? (in $m$)

$A$ $4 \,m$ long ladder leans on a wall to reach a height of $3.2 \,m$ on the wall. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

$A$ boat is sailing with constant speed towards a man sitting on a tree on the river bank. At some moment,the man measures the angle of depression of the boat as $30^{\circ}$. $10$ minutes later,this angle is measured as $60^{\circ}$. How much longer will the boat now take to reach the bank? (in $min$)

$A$ pole $6\, m$ high casts a shadow $2 \sqrt{3}\, m$ long on the ground. Then,the Sun's elevation is: (in $^{\circ}$)