trigonometry(height and distance)

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The shadow of a tower when the angle of elevation of the sun is 45 degree is found to be 5m longer when it is 60 degree. Find the height of the tower.

  • trigonometry(height and distance) -

    sin45=h/(d)
    sin60=h/(d+5)

    h/d=.707
    h/(d+5)=.866

    d=h*1.414
    so
    h=(h*1.414+5)*.866
    solve for h

  • trigonometry(height and distance) -

    the wording of the problem is awkward, but a steeper angle means a shorter shadow

    h/(s + 5) = tan(45º) ... h = s + 5
    ... s = h - 5

    h / s = tan(60º)

    h = h tan(60º) - 5 tan(60º)

    5 tan(60º) = h [tan(60º) - 1)

  • trigonometry(height and distance) -

    The distance should be 5m LONGER at 45o.
    Tan 45 = h/(d+5).
    h = (d+5)*Tan45 = d+5.

    Tan60 = h/d.
    h = d*Tan60 = 1.73d

    d+5 = 1.73d.
    d = 6.83 m.

    h = d + 5 = 6.83+5 = 11.83 m.

  • trigonometry(height and distance) -

    I agree.

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