Answer
$$\angle C = 50 ^o$$ $$c = 2.57 \space and \space a = 1.31$$
Work Step by Step
1. Find the last angle.
$$100 ^{o} + 30^o + \angle C = 180^o$$ $$\angle C = 180^o - 30^o - 100^o = 50 ^o$$
2. Use the law of sines to calculate $a$ and $b$:
$$\frac{sin \space 100^o}{c} = \frac{sin \space 30^o}{a} = \frac{sin \space 50 ^o}{2}$$ $$c = \frac{sin \space 100 ^o}{sin \space 50^o} \times 2 \approx 2.57$$ $$a = \frac{sin \space 30 ^o}{sin \space 50^o} \times 2 \approx 1.31$$
