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 $20m$ 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 $hm$ be the height of tree $CD$ and $xm$ be the width of river.

In $\Delta BCD$
$\tan 60^{\circ }=\frac{CD}{BC}$
$\Rightarrow \sqrt{3}=\frac{h}{x}$
$\Rightarrow h=\sqrt{3}x...(i)$
and in $△ACD$
$\tan 30^{\circ }=\frac{CD}{AC}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20}$
$\Rightarrow x+20=h\sqrt{3}$
$\Rightarrow 3x=x+20$ [using Eq. (i)]
$\Rightarrow x=10$
$\therefore$ Width of river $=10m$