Atriangle 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