Identify the Largest Angle of Triangle ABC

Question

Ok, so I have triangle ABC and the AC is 9, AB is 11 and BC is 10.

How do I know which one is the greatest angle??

Answer 1

Largest angle is opposite the longest side. C is opposite side AB. C is largest angle.

The law of sines says the ratio of the sine of an angle to the side opposite that angle is a constant. It's the same for each of the three angles and their opposite sides:

IF the angle is largest, it's sine is largest and its opposite side has to be largest for the ratio of all 3 angles to opposite sides to be constant.