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 $60^{\circ}$ and when he retires $40$ meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is

• A. 20 m
• B. 30 m
• C. 40 m
• D. 60 m

Answer 1

Answer: (A)

20 m

Answer 2

$tan30^{\circ} = \frac{h}{40+b}$ $\Rightarrow \sqrt{3}\,h = 40+b\quad\quad\dots..\left(1\right)$ $tan60^{\circ} = h/b ? h = \sqrt{3}\,b\quad \quad \dots ..\left(2\right)$ $? b = 20 \,m$