Question

Pre-Cal Help!! (Image Attached)

Answer 1

Note that 165 deg can be split up into 2 angles:  120 and 45 degrees.
We know (or should know) the sine and cosine values of each of these.

sin (x+y) = sin x cos y + cos x sin y

Here,

sin (165) = sin 120 cos 45 + cos 120 sin 45, or
sin (165) =   sqrt(3)/2 * 1/sqrt(2) + 1/2 * 1/sqrt(2)

Finish this work; it will give you the correct answer.