\(A = 24^\circ, B = 80^\circ, c = 20\)
At first glance it might appear that we do not have a side/sine pair. But we can easily get the angle \(C\) opposite the given side and then apply the Law of Sines. This problem is of the type SAA.
\(C = 180^\circ - 24^\circ - 80^\circ = 76^\circ\)
We use the law of sines to find sides \(a\) and \(b\).
\(\dfrac{a}{\sin 23^\circ}=\dfrac{20}{\sin 76^\circ}\)
\(a=\dfrac{20\sin24^\circ}{\sin76^\circ}=8.38\)
\(\dfrac{b}{\sin 80^\circ}=\dfrac{20}{\sin 76^\circ}\)
\(b=\dfrac{20\sin80^\circ}{\sin76^\circ}=20.30\)
So the solution is
| \(C=76^\circ\) |
| \(a=8.38\) |
| \(b=20.30\) |