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Math Help - Optimization problem - a question implying the solving process

  1. #1
    Member dokrbb's Avatar
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    Optimization problem - a question implying the solving process

    I found this problem with the provided solution.
    I already solved such type of problem, but using the triangle similarities and applying the Pythagorean theorem. This solution, however, is shorter. The only thing I can't get is how have got this (see in Bold below). Can someone elaborate a little bit more steps out there(on how we get from what equals tan A to the value of A in degrees)?

    Thanks,

    A fence 6 feet tall runs parallel to a tall building at a distance of 5 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

    Let:
    A = the angle the ladder makes with the ground
    L = length of the ladder

    L = 6/sinA + 5/cosA

    dL/dA = -6cos/sin^2A + 5sinA/cos^2A = 0

    -6cos^3A + 5sin^3A = 0

    sinA/cosA = tanA = (6/5)^(1/3) = 1.06266

    A = 46.73997 degrees


    6/sinA = 8.23892

    5/cos A = 7.29596

    L = 8.23892 + 7.29596 = 15.53488 F
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  2. #2
    Member dokrbb's Avatar
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    Re: Optimization problem - a question implying the solving process

    sinA/cosA = tanA = (6/5)^(1/3) = 1.06266

    A = 46.73997 degrees


    can you help please , it's not actually that I don't know how to calculate (maybe it's this, too.. ) but it's because I get A = 60 something degrees and not 46+
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