Imagine this as a circle. The circle will have a radius of 17mi and the lighthouse will be in the middle. The area of the circle will be the area over which the beacon can be seen.
\(A=\pi r^{2}\) is the equation for the area of the circle where A is the area.
Now we simply plug in our information
A=\(\pi (17)^{2}\)
A=907.9\(mi^{2}\)