The Law of Sines & The Law of Cosines

Question

The triangle below has sides with lengths a = 52, b = 70, and c = 73.

Find the measure of the largest angle.

Round to the nearest thousandth.

The largest angle is approximately __?__  °

Answer 1

largest angle is opposite the largest side

c^2 = a^2 + b^2 - 2abcosC

73^2 =52^2 + 70^2 - 2(52)(70)cosC

=2704 + 4900 - 7280cosC

cosC = (7604 - 5329)/7280 = 2275/7280 = 0.3125

C = cos^-1(0.3125) = 71.790 degrees

Answer 2

Based on Cos rule:

73²=70²+52²-2 x 52 x 70 x Cos θ

θ=71.79º