# maths

posted by Ruth

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.

1. Steve

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)

2. Reiny

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)

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