#### Answer

19 cm

#### Work Step by Step

The law of cosines is:
$a^{2}=b^{2}+c^{2}-2bc\cos A$
where $b,c$ are the two known sides of the triangle while $A$ is the known angle. The unknown side opposite the known angle is $a$.
Substituting the values in the formula and solving:
$a^{2}=b^{2}+c^{2}-2bc\cos A$
$a^{2}=5^{2}+21^{2}-2(5)(21)\cos 60$
$a^{2}=25+441-210\cos 60$
$a^{2}=466-210\cos 60$
We know that $\cos 60^{\circ}=0.5$. Therefore,
$a^{2}=466-210\cos 60$
$a^{2}=466-210(0.5)$
$a^{2}=466-105$
$a^{2}=361$
$a=\sqrt {361}$
$a=19$
Therefore, the length of the unknown side of the triangle is 19 cm.