A person standing on the bank of a river observes that the angle subtended by a tree on the opposite of bank is `60^(@)`. When he retires 40 m.from the bank, he finds the angle to be `30^(@)`. What is the breadth of the river ?

Options

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

Answer

D

Explanation

In `DeltaABC, tan 60^(@)=(h)/(x)`
`rArr sqrt(3)=(h)/(x)rArr h = sqrt(3)x " " ....(1)`
In `DeltaABD, tan 30^(@)=(h)/(x+40)`
`rArr (1)/(sqrt(3))=(h)/(x+40)rArr x + 40 = sqrt(3)h " " ...(2)`
Putting value of h from equation (1), we get
x+40=3x
x=20m