Trigonometry (11th Edition) Clone

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

Chapter 7 - Test - Page 353: 6a

Answer

If $b \gt 10$, then $0 \lt A \lt 30^{\circ}$ and the angle $A$ has exactly one value.

Work Step by Step

Since $B = 150^{\circ}$, then $0 \lt A \lt 30^{\circ}$, otherwise, no such triangle exists. We can use the law of sines to determine the values for $b$: $\frac{b}{sin~B} = \frac{a}{sin~A}$ $sin~A = \frac{a~sin~B}{b}$ $sin~A = \frac{10~sin~150^{\circ}}{b}$ $sin~A = \frac{5}{b}$ Since $sin~30^{\circ} = 0.5$, then $sin~A \lt 0.5$ $\frac{5}{b} \lt 0.5$ $b \gt 10$ If $b \gt 10$, then $0 \lt A \lt 30^{\circ}$ and the angle $A$ has exactly one value.
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.