# Thread: Largest angle of a triangle

1. ## Largest angle of a triangle

Triangle ABC has side lengths a,b and c. If these lengths satisfy a^2=a+2b+2c and 3=a+2b2c, what is the measure (in degrees) of the largest angle?
I applied a bit of cosine rule and sine rule, but all it gave was nasty equations in angles of the triangle.

2. ## Re: Largest angle of a triangle

If it helps... the largest angle is opposite the largest side.

3. ## Re: Largest angle of a triangle

There must be a unique triplet of numbers a b c that satisfies those two equations. By trial and error, I'm pretty sure I found it.

a=5 b=3 c=7

From that it's easy to find the measure of the largest angle using the law of cosines.

So far I can't solve those equations systematically though.

4. ## Re: Largest angle of a triangle

Adding the two equations you get a^2 - 3 = 2a +4b. At a = 3, b becomes zero. So a must be greater than 3.
At a = 4 , b = 5/4 . If you put this value in the first equation, you get negative c which is not possible.
At a = 5, b= 3 and c = 7.