arithmetic

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2. A person walking along a straight road observed that at two consecutive kilometre stones the angles of elevation of a hill front of him are 40o and 80o respectively. Find the height of the hill.

  • arithmetic -

    Make a sketch

    I have A, B, and C on a horizontal line, and H as the top of the hill
    Angle A = 40° and angle HBC - 80°, AB = 2 km
    In triangle ABH, angle ABH = 100°
    then angle AHB = 40°
    which makes BH = 2 , (isosceles triangle)
    (that was lucky, else I would need the sine law to find BH)

    in triangle HBC (right-angled)
    sin 80 = HC/2
    HC = 2sin80 = 1.97 km

    Wow, that is more than just a "hill"

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