# Chapter 11 - Section 11.1 - The Sine Ratio and Applications - Exercises - Page 505: 36c

$94.0 in^2$

#### Work Step by Step

The length of segment BC is: $sin( 90 - \beta) = \frac{CB}{AB}$ $AB sin( 90 - \beta) = CB$ $CB=sin(90-55)(20 in)=11.5 in$ We now find the length of the other side: $sin( \beta) = AC/AB$ Simplifying, we find: $ABsin( \beta) = AC$ This gives: $AC=20(sin(55))=16.4 in$ Using the area formula: $A=.5bh$ $A=.5(16.4)(11.5)$ $A=94.0 in^2$

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