Question

Find the measure of angleC in the following triangle

Answer 1

C = 58.88 degrees

Explanation:

We can use the law of cosines to find the missing angle measurement

c^2 = a^2 +b^2 -2ab cosC

Rearranging and solving for cos C

2ab Cos C = a^2 +b^2 - c^2

Divide by 2ab

cos(C) = a^2 + b^2 − c^2

------------------------

2ab

Substituting what we know a = 31 b = 21 c = 27

31^2 + 21^2 - 27^2

cos C = -----------------------------

2(31)(21)

cos C = .516897081

Take the inverse cos on each side

cos^-1 cos C = cos ^-1 (.516897081)

C = 58.88 degrees