The figure shows the location of three points around a lake. The length of the lake, BC, is also shown. (The figure is not drawn to scale.)

A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 6 miles. The length BC of the triangle is labeled as 2 miles. This length BC is also the length of an irregular gray shaded shape.

Which of the following choices is closest to the distance (in miles) between points A and B?

3.46 miles
5.66 miles
6.32 miles
7.75 miles