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Math Help - to prove a longer side correspond a greater opposite angle

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    to prove a longer side correspond a greater opposite angle

    I"ve got a question. it is not difficult for us to accept that 'in a triangle, a longer side correspond a greater opposite angle'. however, how can we prove that? Is it possible for me to use sine formula to prove?
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    Quote Originally Posted by ling_c_0202
    I"ve got a question. it is not difficult for us to accept that 'in a triangle, a longer side correspond a greater opposite angle'. however, how can we prove that? Is it possible for me to use sine formula to prove?
    I would imagine you can do so. You might find a quicker proof using the Law of Cosines, though.

    -Dan
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    Quote Originally Posted by ling_c_0202
    I"ve got a question. it is not difficult for us to accept that 'in a triangle, a longer side correspond a greater opposite angle'. however, how can we prove that? Is it possible for me to use sine formula to prove?
    It is rather basic. Difficult to explain without a diagram. What you do is construct a triangle with equal angles (thus equal sides) on the side of the triangle. Then you use the fact "The whole is greater than the sum of its parts).
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