Answer
The distance from Matt to the balloon is $x \approx 394.4$ ft.
Work Step by Step
1. Find the missing angle of the triangle
$= 180 - (65+47)$
$= 180 - 112$
$= 68^{\circ}$
2. Use the Law of Sines to find $x$
$\frac{x}{sin(47)} = \frac{500}{sin(68)}$
$x = \frac{500sin(47)}{sin(68)}$
by GDC / calculator
$x = 394.3951...$ ft
$x \approx 394.4$ ft
