Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 7 - Section 7.3 - The Ambiguous Case - 7.3 Problem Set - Page 390: 16

Answer

$B = 114.66^\circ \hspace{10pt} A =63.16^\circ \hspace{10pt} a = 806.068\,m$ $B' = 114.66^\circ \hspace{10pt} A' = 13.84^\circ \hspace{10pt} a' = 216.101 \, m$

Work Step by Step

$\sin{B} = \dfrac{b \sin{C}}{c} = \dfrac{821 \sin{(51.5^\circ)}}{707}$ $\sin{B} = 0.908$ $B = 65.34^\circ\hspace{40pt} B' = 114.66^\circ$ $A = 180-(B+C) = 63.16^\circ$ $a = \dfrac{c \sin{A}}{\sin{C}} = \dfrac{707 \times \sin{63.16}}{\sin{51.5}}$ $a = 806.068 \,m$ $B' + C < 180 \hspace{10pt} \therefore B'$ is valid. $A' = 180-(B+C') = 13.84^\circ$ $a' = \dfrac{c \sin{A'}}{\sin{C}} = \dfrac{707 \times \sin{13.84}}{\sin{51.5}}$ $a' = 216.101 \, m$
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