Posted by **Ruth** on Thursday, October 17, 2013 at 12:34pm.

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.

- maths -
**Steve**, Thursday, October 17, 2013 at 12:44pm
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)

- maths -
**Reiny**, Thursday, October 17, 2013 at 12:51pm
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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