There is an angle 𝜃 such that sin 𝜃 = 3/5 and cos 𝜃 = 4/5. In a triangle assume that angle 𝛼 is opposite side a, 𝛽 is opposite b, and 𝛾 is opposite c. Assume that 𝛼 = 𝜃, that b = 3, and that c = 5. Find the length of side a.

Answer 1

using the law of cosines,
a^2 = b^2 + c^2 - 2bc cos𝜃
so plug in your numbers

Answer 2

How do I do that if I don't know what 𝜃 equals?

Answer 3

really? Who said you have to know 𝜃?
Did you read what you posted? cos𝜃 = 4/5
so use that!