Elementary Geometry for College Students (7th Edition)

The distance from Matt to the balloon is $x \approx 394.4$ ft.
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