What are the measures of all three angles of triangle ABC with side lengths 8,11, and 17?

For this use cosine law;

c^2 = a^2 + b^2 - 2abCosC.

Label your sides, we'll use

a = 8

b = 11

c = 17

289 = 64 + 121 - 2 (8) (11) CosC

289 = 185 - 176CosC

104 = - 176CosC

.59 = CosC

That's just your first angle. For the rest do the same formula, plug in your values and get your answer. You can also use sin law once you have what's already here, however it's good to practice using cosine law.