## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 7 - Quiz (Sections 7.1-7.3) - Page 325: 7

#### Answer

The angles of the triangle are as follows: $A = 111^{\circ}, B = 41.0^{\circ},$ and $C = 28.0^{\circ}$ The lengths of the sides are as follows: $a = 648, b = 456,$ and $c = 326$

#### Work Step by Step

$c = 326$ $A = 111^{\circ}$ $B = 41.0^{\circ}$ We can find angle $C$: $A+B+C = 180^{\circ}$ $C = 180^{\circ}-A-B$ $C = 180^{\circ}-111^{\circ}-41.0^{\circ}$ $C = 28.0^{\circ}$ We can use the law of sines to find the length of side $b$: $\frac{b}{sin~B} = \frac{c}{sin~C}$ $b = \frac{c~sin~B}{sin~C}$ $b = \frac{(326)~sin~(41.0^{\circ})}{sin~28.0^{\circ}}$ $b = 456$ We can use the law of sines to find the length of side $a$: $\frac{a}{sin~A} = \frac{c}{sin~C}$ $a = \frac{c~sin~A}{sin~C}$ $a = \frac{(326)~sin~(111^{\circ})}{sin~28.0^{\circ}}$ $a = 648$

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