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November 14th, 2015, 07:46 PM  #1 
Newbie Joined: Nov 2015 From: India Posts: 14 Thanks: 1  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?

November 14th, 2015, 09:41 PM  #2 
Senior Member Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177 
Any triangle with sides (3k, 4k, 5k) is right triangle, where k is any positive integer.

November 15th, 2015, 12:11 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,823 Thanks: 2160 
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. 
November 15th, 2015, 04:50 AM  #4 
Newbie Joined: Nov 2015 From: India Posts: 14 Thanks: 1 
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. 
November 15th, 2015, 06:17 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,823 Thanks: 2160 
No, but sin($\angle$BAD):sin($\angle$CAD) = (AC/AB)BD:CD.


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