Question

On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of $60^{\circ}$ at the top of the tree. The angle of elevation of the top of the tree at a distance $20\, m$ away from the bank is $30^{\circ}$. The width of the river is

• A. 20 m
• B. 10 m
• C. 5 m
• D. 1 m

Answer 1

Answer: (B)

Let $h m$ be the height of tree $C D$ and $x m$ be the width of river.

In $\Delta B C D$
$\tan60^{\circ}=\frac{C D}{B C}$
$\Rightarrow \sqrt{3}=\frac{h}{x}$
$\Rightarrow h=\sqrt{3} x\,\,\,...(i)$
and in $\triangle A C D$
$\tan 30^{\circ}=\frac{C D}{A C}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20}$
$\Rightarrow x+20=h \sqrt{3}$
$\Rightarrow 3 x=x+20\,\,\,\,$ [using Eq. (i)]
$\Rightarrow x=10$
$\therefore $ Width of river $=10 \,m$