Answer
$40^{\circ}$
Work Step by Step
We can use the law of cosines to find the unknown angle.
The law of cosines is:
$a^{2}=b^{2}+c^{2}-2bc\cos \theta$
where $a,b,c$ are the three sides of the triangle while $\theta$ is the angle opposite the side $a$.
Substituting the values in the formula and solving:
$a^{2}=b^{2}+c^{2}-2bc\cos \theta$
$13^{2}=16^{2}+20^{2}-2(16)(20)\cos \theta$
$169=256+400-640\cos \theta$
$169=656-640\cos \theta$
$169-656=-640\cos \theta$
$-487=-640\cos \theta$
$-640\cos \theta=-487$
$\cos \theta=\frac{-487}{-640}$
$\cos \theta=\frac{487}{640}$
$\theta=\cos^{-1} \frac{487}{640}$
$\theta=40.45^{\circ}\approx40^{\circ}$
