Answer
$$\angle C = 114 ^o$$ $$b \approx 24 $$ $$a \approx 51$$
Work Step by Step
1. Find the last angle.
$$46 ^{o} + 20^o + \angle C = 180^o$$ $$\angle C = 180^o - 46^o - 20^o = 114 ^o$$
2. Use the law of sines to calculate $a$ and $b$:
$$\frac{sin \space 46^o}{a} = \frac{sin \space 20^o}{b} = \frac{sin \space 114 ^o}{65}$$ $$b = \frac{sin \space 20 ^o}{sin \space 114^o} \times 65 \approx 24$$ $$a = \frac{sin \space 46 ^o}{sin \space 114^o} \times 65 \approx 51$$
