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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 -

    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 -

    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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