I think you mean to say

. If

is in the third quadrant, then

and

. Recall that

We expect

to be negative, so we take the negative root. We end up with

We also know to expect

, so

By definition, we have

and so
24 foot board... I added a picture for the break down
3*x
3*2
3x+6
5*x
5*-8
5x-40
Story short the answer is 25
We need to use Law of sine.
sin A/a = sin C/c
sin A/|CB| = sin C/|AB|
sin A/14 = sin(118⁰)/ 20
sin A = (14*sin(118⁰))/ 20
A=arcsin((14*sin(118⁰))/ 20) ≈ 38⁰
It's 82 degrees. Subtract your minor arc (98) by 360 to get your major arc, which is 262. Then, subtract 98 (minor arc) from 262 (major arc), which gives you 164. Finally, divide 164 by 2 to get angle ABC.