A triangle has sides of length 5, 8, and 10. What is the measure of its largest angle?

We'll use the Law of Cosines

We'll call

side a = length 5

side b = length 8

side c = length 10

and their corresponding angles as A, B and C

"C" would be the largest angle

cos (C) = (a^2 + b^2 - c^2) / 2 * a * b

cos (C) = (5^2 + 8^2 - 10^2) / 2 * 5 * 8

cos (C) = 25 + 64 - 100 / 80

cos (C) = - 11 / 80

cos (C) = - 0.1375

arc cosine (-0.1375) = 97.903 Degrees

The largest angle is 97.903 Degrees