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Math Help - Triangle Trig Question

  1. #1
    Member ~berserk's Avatar
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    Triangle Trig Question

    Last One!

    A farmer has a triangular field with sides of 240 ft., 300 ft., and 360 ft. He wants to apply fertilizer to the field. If one 40-pound bag of fertilizer covers 6000 square feet, how many bags must he buy to cover the field.
    I drew a diagram and have a feeling I need to use these equations
    Law of Cosines
    Area of a triangle (1/2 ab sinC)

    I just don't know how I would go about it
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  2. #2
    Member
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    Quote Originally Posted by ~berserk View Post
    Last One!

    A farmer has a triangular field with sides of 240 ft., 300 ft., and 360 ft. He wants to apply fertilizer to the field. If one 40-pound bag of fertilizer covers 6000 square feet, how many bags must he buy to cover the field.
    I drew a diagram and have a feeling I need to use these equations
    Law of Cosines
    Area of a triangle (1/2 ab sinC)

    I just don't know how I would go about it
    Use Cosine rule to get the angle opposite one of the sides.

    240^2 = 300^2 + 360^2 - 2*300*360CosA

    CosA = (300^2 + 360^2 - 240^2)/(2*300*360)

    A = Cos^-1(3/4)

    Area = 0.5*300*360Sin(Cos^-1(3/4)) = 35718 sq ft

    35718 / 6000 = 5.953

    Therefore he needs 6 bags.
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