A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is `60^(@)`. The angle of elevation is `30^(@)` from a point at a distance y m from the bank of the river. What is the height of the tree ?

Options

A. y m
B. 2y m
C. `(sqrt(3)y)/(2)m`
D. `(y)/(2)m`

Answer

C

Explanation

Let DC be the tree of height h metre. Let a man is standing on the point B (bank of a river).
Let BC=x and angle of elevation i.e. `angleDBC=60^(@)`.
Also, let AB=y and `angleDAC=30^(@)`.
In `DeltaACD`,

`tan 30^(@) = (CD)/(AC)`
`rArr (1)/(sqrt(3))=(h)/(x+y)`
`rArr x+y=hsqrt(3) " " .......(i)`
`tan 60^(@)=(CD)/(BC)rArr sqrt(3)=(h)/(x)`
`rArr x=(h)/(sqrt(3)) " " ........(ii)`
From eqns. (i) and (ii),
`(h)/(sqrt(3))+y=hsqrt(3)`
`rArr y=h (sqrt(3)-(1)/(sqrt(3)))=(2h)/(sqrt(3)) rArr h= (sqrt(3)y)/(2)m`