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

The Correct Option is A

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.