Question

A person, standing on the bank of a stream, observes that the angle subtended by a plant on the opposite bank is 60${}^0$. When he moves 50 m away from the bank, he finds that the angle of elevation to be 30${}^0$. Find the breadth of the stream.

• A. 40 m
• B. 35 m
• C. 45 m
• D. 30 m
• E. 25 m

Answer 1

The correct option is E

25 m

Let AB be the width of the stream and BC be the plant which makes an angle of 60${}^0$ at a point A on the opposite bank. Let D be the position of the person after retreating 50 m from the bank. Let AB = `x' metres and BC = `h' metres.

From right angled triangles ABC and DBC, we have -

tan 60${}^0$ = $\frac{CB}{AB}$and tan 30${}^0$ = $\frac{BC}{DB}$

$\Rightarrow \sqrt{3}=\frac{h}{x}and\frac{1}{\sqrt{3}}=\frac{h}{x+50}$

$\Rightarrow h=x\sqrt{3}$and h = $\frac{x+50}{\sqrt{3}}$

$\Rightarrow x\sqrt{3}=\frac{x+50}{\sqrt{3}}$

$\Rightarrow$3x = x + 50

$\Rightarrow$ x = 25 m

Hence, the breadth of the stream is 25 m.