Answer
$a = 40$
$b = 20\sqrt 3$
$\angle C = 30 ^o$
Work Step by Step
Cosine definition: $$cos \space 60^o = \frac{20}{a}$$ $$a = \frac{20 }{cos \space 60 ^o} = \frac{20}{\frac 12} = 40$$
Sine definition: $$sin \space 60^o = \frac{b}{a} = \frac{b}{40}$$ $$b = sin \space 60 ^o \space (40) = \Bigg(\frac{\sqrt 3}{2}\Bigg)(40) = 20 \sqrt 3$$
$$\angle A + \angle B + \angle C = 180 ^o$$ $$\angle C = 180^o - 60 ^o - 90 ^o = 30 ^o$$
