# Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 723: 81

The obtuse angle $B\approx 127{}^\circ$.

#### Work Step by Step

Consider the given expression $\cos B=\frac{{{6}^{2}}+{{4}^{2}}-{{9}^{2}}}{2\cdot 6\cdot 4}$. \begin{align} & \cos B=\frac{{{6}^{2}}+{{4}^{2}}-{{9}^{2}}}{2\cdot 6\cdot 4} \\ & \cos B=\frac{36+16-81}{48} \\ & \cos B=-\frac{29}{48} \\ & B={{\cos }^{-1}}\left( \frac{-29}{48} \right) \end{align} This implies $B\approx 127{}^\circ$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.