Question

A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60∘.
Calculate : the width of the river and the height of the tree.

Answer 1

$OB$ is the width of river.

$OB=d$

$OC$ is the height of tree.

$OC=h$

$\tan {30}^{\circ }=\frac{h}{d+50}\Rightarrow h\sqrt{3}=d+50$

$\tan {60}^{\circ }=\frac{h}{d}\Rightarrow h=\frac{d}{\sqrt{3}}$

$\therefore h\sqrt{3}=3d=d+50$

$d=25$

$\therefore h=25\sqrt{3}$

Width of river$=25m$

Height of tree$=25\sqrt{3}m$