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 4 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? (5 points)

Question 7 options:

1)

3.16 miles

2)

3.46 miles

3)

4.47 miles

4)

4.90 miles