Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 322: 49



Work Step by Step

We can use the law of cosines to find the unknown angle. The law of cosines is: $a^{2}=b^{2}+c^{2}-2bc\cos \theta$ where $a,b,c$ are the three sides of the triangle while $\theta$ is the angle opposite the side $a$. Substituting the values in the formula and solving: $a^{2}=b^{2}+c^{2}-2bc\cos \theta$ $13^{2}=16^{2}+20^{2}-2(16)(20)\cos \theta$ $169=256+400-640\cos \theta$ $169=656-640\cos \theta$ $169-656=-640\cos \theta$ $-487=-640\cos \theta$ $-640\cos \theta=-487$ $\cos \theta=\frac{-487}{-640}$ $\cos \theta=\frac{487}{640}$ $\theta=\cos^{-1} \frac{487}{640}$ $\theta=40.45^{\circ}\approx40^{\circ}$
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.