Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 313: 11

$\theta = 120^{\circ}$

Let $a = 3$, let $b=5$, and let $c = 7$. We can use the law of cosines to find $\theta$: $c^2 = a^2+b^2-2ab~cos~\theta$ $2ab~cos~\theta = a^2+b^2-c^2$ $cos~\theta = \frac{a^2+b^2-c^2}{2ab}$ $\theta = arccos(\frac{a^2+b^2-c^2}{2ab})$ $\theta = arccos(\frac{3^2+5^2-7^2}{(2)(3)(5)})$ $\theta = arccos(\frac{-15}{30})$ $\theta = arccos(\frac{-1}{2})$ $\theta = 120^{\circ}$