The shadow of a tower standing on a level ground is found to be 2x meters longer when sun's altitude is 30 degree than when it was 45 degree.Find the height of the tower.

Answer 1

If the tower is h high and the shadow is s long at angle θ, we have

h/s = tanθ, or
s = h/tanθ

So, now we know that

h/tan30 = h/tan45 + 2x
h√3 = h + 2x
h(√3-1) = 2x
h = 2x/(√3-1)

Answer 2

using only the information you gave, sketch two triangles

let the height of the tower be h
let the length of the shadow at 45° be m
then the length of the shadow at 30° is m+2x

tan 45 = h/m and tan 30 = h/(m+2x)
1 = h/m and 1/√3 = h/(m+2x)
m = h and m+2x = h√3

put 1st into 2nd
h + 2x = h√3
h√3 - h = 2x
h(√3-1) = 2x

h = 2x/√3 - 1)