Question

In ∆ABC, a = 20, b = 12, and c = 30. What is the measure of the largest angle to the nearest tenth?

Answer 1

The largest angle is opposite the longest side.

The cosine rule tells us that c^2=a^2+b^2-2abcosC.

900=400+144-2*240cosC; 900-544=-480cosC; cosC=-356/480=-89/120=-0.7417. cos(42.13°)=0.7417. Because cosC is negative the angle is bigger than 90° but less than 180°.

Therefore C=180-42.13=137.87 degrees. To 1 dec place this is 137.9º.