Answer
$53^{\circ}$
Work Step by Step
We can use the law of cosines to find the unknown angle.
The law of cosines is:
$a^{2}=b^{2}+c^{2}-2bc\cos \beta$
where $a,b,c$ are the three sides of the triangle while $\beta$ is the angle opposite the side $a$.
Substituting the values in the formula and solving:
$a^{2}=b^{2}+c^{2}-2bc\cos \beta$
$16^{2}=13^{2}+20^{2}-2(13)(20)\cos \beta$
$256=169+400-520\cos \beta$
$256=569-520\cos \beta$
$256-569=-520\cos \beta$
$-313=-520\cos \beta$
$-520\cos \beta=-313$
$\cos \beta=\frac{-313}{-520}$
$\cos \beta=\frac{313}{520}$
$\beta=\cos^{-1} \frac{313}{520}$
$\beta=52.99^{\circ}\approx53^{\circ}$
