Algebra 2 (1st Edition)

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

Chapter 13, Trigonometric Ratios and Functions - 13.5 Apply the Law of Sines - 13.5 Exercises - Skill Practice - Page 886: 13


$A=37.6^{\circ}; B=38.4^{\circ}, a= 15.7$

Work Step by Step

Law of sines: $\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$ Here, $\dfrac{\sin 104^{\circ}}{25}=\dfrac{\sin B}{16}$ This implies: $B=38.4^{\circ}$ Since a triangle always has $180^{\circ}$, we need to add the known angles together and subtract the result from $180^{\circ}$. Thus, $A=180^{\circ}-(104^{\circ}+38.4^{\circ})=37.6^{\circ}$ Now, $\dfrac{\sin 104^{\circ}}{25}=\dfrac{\sin 37.6^{\circ}}{a}$ $\implies a=\dfrac{25 \sin 37.6^{\circ}}{\sin 104^ {\circ}}=15.7$ Hence, $A=37.6^{\circ}; B=38.4^{\circ}, a= 15.7$
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.