# Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 720: 15

$C=50{}^\circ,a\approx 7.1$ and $b\approx 7.1$.

#### Work Step by Step

First we will find the value of C. Properties of a triangle: The sum of three angles is $A+B+C=180{}^\circ$ \begin{align} & A+B+C=180{}^\circ \\ & 65{}^\circ +65{}^\circ +C=180{}^\circ \\ & C=180{}^\circ -130{}^\circ \\ & C=50{}^\circ \end{align} Now, we will find the remaining sides using the ratio $\frac{c}{\sin C}$,or $\frac{6}{\sin 50{}^\circ }$, Now, we will use the law of sines to find a. \begin{align} & \frac{a}{\sin A}=\frac{c}{\sin C} \\ & \frac{a}{\sin 65{}^\circ }=\frac{6}{\sin 50{}^\circ } \\ & a=\frac{6\sin 65{}^\circ }{\sin 50{}^\circ } \\ & a\approx 7.1 \end{align} Using the law of sines again, we will find b. \begin{align} & \frac{b}{\sin B}=\frac{c}{\sin C} \\ & \frac{b}{\sin 65{}^\circ }=\frac{6}{\sin 50{}^\circ } \\ & b=\frac{6\sin 65{}^\circ }{\sin 50{}^\circ } \\ & b\approx 7.1 \end{align}

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.