Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/4`. If side C has a length of `12` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

`a ~~ 4.39`

Explanation:

Using the notation where the sides are the lowercase letters, a, b, and c and the opposite angles are the uppercase letters, A, B, and C. The law of sines is:

`a/sin(A) = b/sin(B) = c/sin(C)`

We are given:
`c = 12, C = pi/4 and A = pi/12`

Using the first and last part of the law of sines:

`a/sin(A) = c/sin(C)`

`a = (12sin(pi/2))/sin(pi/4)`

`a ~~ 4.39`