Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 19

Answer

See below

Work Step by Step

We are given $a, c, b$. Use law of cosines to find $c$: $$c^2=a^2+b^2-2ac\cos C\\ c=\sqrt a^2+b^2-2ab\cos C\\c\approx 58.21$$ Use law of sines to find: $\frac{\sin B}{b}=\frac{\sin C}{c}\\\sin B=\frac{\sin C}{c}\times b\\\arcsin (\sin B)=\arcsin (\frac{\sin C}{c}b)\\B=\arcsin(\frac{\sin C}{c}. b)\\A\approx 47.28^\circ$ Since the sum of the triangle is $180^\circ$, we obtain: $$A+B+C=180^\circ\\A=180^\circ-A-B\\A=180^\circ -96^\circ -47.28^\circ\\A=36.72^\circ$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.