What is the length of side c, given a = 10, b = 8, and c = 105°? round the answer to the nearest tenth?

For this case, using the law of cosine we have:

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

Substituting values we have:

c ^ 2 = 10 ^ 2 + 8 ^ 2 - 2 * 10 * 8 * cos (105)

Clearing c we have:

c = root (10 ^ 2 + 8 ^ 2 - 2 * 10 * 8 * cos (105))

c = 14.33216827

round the answer to the nearest tenth:

c = 14.3

Answer:

the length of side c is:

c = 14.3