Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6`. If side C has a length of `9` and the angle between sides B and C is `pi/12`, what are the lengths of sides A and B?

Answer 1

A is `C cos (A,C) = 9 cos (pi -5pi/6-pi/12) = 9 cos(6pi/6 -5pi/6 - pi/12) = 9 cos(pi/6 - pi/12) = 9 cos (pi/12) = 8.69`

Explanation:

B is `A cos(pi-pi/6)`
`B = 7.52`

Of course these are lengths, so we take the absolute value.