Math

isoceles triangle with vertex of 45 degrees, base angles are 67.5 degrees. The 2 legs are 10' in length. What is the length of the base? (I am an older adult with minimal math skill. Just have a building project.)

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asked by Tom
  1. In your sketch , draw a perpendicular from the vertex to the base.
    You now have 2 identical right-angled triangles.
    let the base for each be x units (your whole base would then be 2x)

    by simple trig,
    cos 67.5° = x/10
    x = 10cos67.5
    = 3.8268.. , Use your calculator for this

    so twice that is appr 7.654 '
    which would be 7 ' and about 8 inches

    or by the cosine law:
    base^2 = 10^2 + 10^2 - 2(10)(10)cos 45
    = 58.5786..
    base = √58.5786
    = appr 7.654 , same as above

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    posted by Reiny

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