#### Answer

$94.0 in^2$

#### 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:
$A=.5bh$
$A=.5(16.4)(11.5)$
$A=94.0 in^2$