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November 14th, 2015, 07:46 PM   #1
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are angles in the same ratio as the sides of a triangle

If we consider a triangle ABC, where sides a:b:c=3:4:5, then are the angles also in the same ratio 3:4:5?
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November 14th, 2015, 09:41 PM   #2
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Any triangle with sides (3k, 4k, 5k) is right triangle, where k is any positive integer.
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November 15th, 2015, 12:11 AM   #3
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For any triangle ABC with sides a = BC, b = AC and c = AB, a:b:c = sin(A):sin(B):sin(C).

In the example given, 3:4:5 = 3/5:4/5:1.
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November 15th, 2015, 04:50 AM   #4
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Ok got it. Another question, if we consider a triangle ABC where AD intersects BC such that BD=2CD, then can we determine the ratio in which angle BAC is divided into angle BAD and CAD. I mean can we find BAD:CAD?

Last edited by skipjack; November 15th, 2015 at 05:31 AM.
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November 15th, 2015, 06:17 AM   #5
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No, but sin($\angle$BAD):sin($\angle$CAD) = (AC/AB)BD:CD.
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