A man of height `=3//2m`,wants to see himself in plane mirror from top to bottom. The plane mirror is inclined with vertical wall at angle `alpha=53^(@)`. If the least size of mirror to see him `3/n m`, the distance of eye from mirror is `d=3m`, find the value of `m`

Answer

8

Explanation

`h/d=tantheta`
Using triangle `EAB`
`(d/(costheta))/(sin{90-(alpha+theta)})=H/(sin2theta)`
`impliesd/(cos(alpha+theta))=H/(2sintheta)`
`implies 2d=H[cosalpha cot theta-sin alpha]`
`=Hcos alpha (d/h)-Hsin alpha`
`impliesh=(Hd cos alpha)/(2d+H si alpha)=(3/2xx3xx3/5)/(2xx3+3/2xx4/5)=27/(36xx2)=3/8`