## Trigonometry (10th Edition)

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.