A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is `60^@`. When he retires 80 m from the corner, along the same straight line, he finds the angle to be `30^@`. The length of the field is

Options

A. 20
B. `40sqrt2`
C. 40
D. `20sqrt2`

Answer

D

Explanation

यहाँ PORS वर्गाकार मैदान है जिसमें PR विकर्ण की लंबाई x माना

`thereforeDelta` APR में
`tan60^(@)=(AR)/(PR)`
`rArrAR=PRtan60^(@)=sqrt3x`
`thereforeDelta` ABR में
`tan30^(@)=(AR)/(BR)`
`1/(sqrt3)=(sqrt3x)/(80+x)`
`rArr80+x=3x`
`rArr2x=80` तथा `thereforex=40m`
`therefore` मैदान की लंबाई = `("विकर्ण")/(sqrt2)=40/(sqrt2)=20sqrt2m`