Answer
$AB\approx679$ft
Work Step by Step
One first must find the angle $B$ using the law of sines:
$\frac{sin(B)}{312}=\frac{sin(48.6º)}{527}$ solving for $B$ leads to:
$B=$sin$^{-1}($sin$(48.6º) \cdot \frac{312}{527})$
$B=26.4º$
The sum of all angles in a triangle is equal to 180º, so:
$A+B+C=180º$
$C=180º-48.6º-26.4º=105º$
Now one can find the distance $AB$ using, once again, the law of sines:
$\frac{sin(105º)}{AB}=\frac{sin(48.6º)}{527}$
$AB=527\cdot \frac{sin(105º)}{sin(48.6º)}$
$AB\approx679$ft
*Triangle is not drawn to scale
