Answer
63.7
Work Step by Step
Using the law of cosines, we find:
$$ a^2=b^2+c^2-2bc\cdot \cos \left(\alpha \right) \\ a=\sqrt{b^2+c^2-2bc\cos \left(α\right)}\\ a=\sqrt{60.5^2+90^2-2\cdot \:60.5\cdot \:90\cos \left(45^{\circ \:}\right)}\\ a=63.7$$
