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Math Help - Find the angles of the triangle?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find the angles of the triangle?

    Each of the two triplets of numbers (a, b, c)\ \& \left(\frac{a}{2b},\ \frac{2b}{3c},\ \frac{3c}{a}\right) is a Geometric Progression. Can the numbers a,b,c be the lengths of the sides of a triangle? If they can what triangle is it? Find the angles of the triangle.
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by fardeen_gen View Post
    Each of the two triplets of numbers (a, b, c)\ \& \left(\frac{a}{2b},\ \frac{2b}{3c},\ \frac{3c}{a}\right) is a Geometric Progression. Can the numbers a,b,c be the lengths of the sides of a triangle? If they can what triangle is it? Find the angles of the triangle.
    Use the fact that they are in a GP, the two equations ( b^2 = ac and \frac{4b^2}{9c^2} = \frac{a}{2b}\frac{3c}{a})to get 9c = 4a = 6b. They clearly form a triangle. As for the angles, compute them for the triangle with sides 4,6,9.
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