If the height of a tower and the distance of the point of observation from its foot, both are increased by `10%`, then the angle of elevation of its top remains unchanged.

Explanation

True,
Case I Let the height of a tower be h and the distance of the point of observation from its foot is x.
In `DeltaABC`,
`tantheta^(1) = (AC)/(BC) = h/x` .............(i)

Case II Now, the heightof a tower increased by `10%=h + 10%` of h`=h + h xx 10/100= (11h)/10`
and the distance of the point of observation from its foot.`=x + 10%` of x
`=x+x xx 10/100= (11x)/10`
In `DeltaPQR, tantheta_(2) =(PR)/(QR) ((11h)/(10))/((11x)/(10))`
`rArr tantheta_(2)=h/x`

`rArr theta_(2) = tan^(-1)(h/x)`………….(ii)
From Eqs. (i) and (ii),
`theta_(1) = theta_(2)`
Hence,the required angle of elevation of its top remains unchanged.