Answer
$x^{o} \approx60.5 $
Work Step by Step
Apply law of cosines $a^2=b^2+c^2-2bc \cos A$
Need to solve for a.
That is, $a=\sqrt {b^2+c^2-2bc \cos A} $
Plug the given values to obtain:
$a=\sqrt {(60)^2+(68)^2-2 \times 60 \times 68 \cos 20^{o}} \approx 23.6$
In order to calculate the value of $B$, we will use $B =x^{o}$.
$\dfrac{\sin B}{b}=\dfrac{\sin A}{a} \implies B=\sin^{-1} (\dfrac{b \sin A}{a}) $
or, $x^{o}=\sin^{-1} (\dfrac{60 \sin 20^{o}}{23.6}) \implies x^{o} \approx60.5 $
