By what percentage will be transmission range of a TV tower be affected when the height of the tower is increased by 21% ?

Explanation

Original transmission as coverage area,
`d = sqrt(2hR)`
where , d = distance to horizon, R = radius of earth and h = height of tower.
` because` Nwe height,
`h. = h + 21% ` of `h = h + 21/100 h = 1.21h`
New transmission range,
`d. = sqrt(2h. R)`
` because (d.)/(d) = sqrt((h.)/(h)) = sqrt(1.21) = 1.1`
` therefore` Increase in range ,
`(Delta d)/(d) xx 100 = (d. - d)/(d) xx 100 = ((d.)/(d) - 1) xx 100`
` = (1.1 - 1) xx 100 = 10%`