Solving a triangle with3 known sides?

Question

I need to solve this triangle. I don't know any of the angles but the known sides are a = 27, b = 21, and c = 24. Obviously I need to find all the angles. Please show your work. Thanks!

Answer 1

Use the law of Cosines

a² = b² + c² - 2bc cosA

So Angle A is

A = arccos((a²-b²-c²)/(-2bc))

You can do the exact same thing for angles B & C, or since you have angle A above, you can use the law of sines.