Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 600 and when he walks 40 metres away from the tree the angle of elevation becomes 300. The breadth of the river is

• A. 20m
• B. 30m
• C. 40m
• D. 60m

Answer 1

Answer: (A)

20m

Answer 2

From the bank:

$\tan(60°) = \frac{h}{d} \quad \Rightarrow \quad h = \sqrt{3}d$

After moving 40 m:

$\tan(30°) = \frac{h}{d + 40} \quad \Rightarrow \quad \frac{1}{\sqrt{3}} = \frac{\sqrt{3}d}{d + 40}$

$\therefore$ d is equal to,

$d + 40 = 3d \\\ \Rightarrow d = 20 \, \text{meters}$

The breadth of the river is 20 meters.