Thread: 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?

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

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).