# Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 720: 11

$A=80{}^\circ,a\approx 39.5$ and $c\approx 10.4$.

#### Work Step by Step

First we will find the value of A Properties of the triangle: Sum of three angles is $A+B+C=180{}^\circ$ \begin{align} & A+B+C=180{}^\circ \\ & A+85{}^\circ +15{}^\circ =180{}^\circ \\ & A=180{}^\circ -100{}^\circ \\ & A=80{}^\circ \end{align} Now, we will find the remaining sides using the ratio $\frac{b}{\sin B}$,or $\frac{40}{\sin 85{}^\circ }$, Now, we will use the law of sines to find a. \begin{align} & \frac{a}{\sin A}=\frac{b}{\sin B} \\ & \frac{a}{\sin 80{}^\circ }=\frac{40}{\sin 85{}^\circ } \\ & a=\frac{40\sin 80{}^\circ }{\sin 85{}^\circ } \\ & a\approx 39.5 \end{align} Using the law of sines again, we will find c. \begin{align} & \frac{c}{\sin C}=\frac{b}{\sin B} \\ & \frac{c}{\sin 15{}^\circ }=\frac{40}{\sin 85{}^\circ } \\ & c=\frac{40\sin 15{}^\circ }{\sin 85{}^\circ } \\ & c\approx 10.4 \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.