A vertical tower PQ subtends the same anlgle of `30^@` at each of two points A and B ,60 m apart on the ground .If AB subtends an angle of `120^@` at p the foot of the tower ,then find the height of the tower .

Options

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Answer

B

Explanation

Let PQ =h and PB =x =PA
then tan `30^(@) =(h)/(x) rArr (1)/(sqrt(3)) =(h)/(x)`
`rArr x=sqrt(3)h`
using sine rule in `DeltaPAB`
`(PA)/("sin"30^(@)) =(AB)/("sin"120^(@))`
`rArr x=(60."sin" 30^(@))/("sin" 120^(@))`
`rArr sqrt(3) h=60 xx 1/2 x 2/sqrt(3)`
`rArr h =20 m`