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 5 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?

1.73 miles
2.65 miles
3.16 miles
4.58 miles

AB would equal 4.58 miles.

You can set this question up by drawing a right triangle and labeling your points ABC, next you want to place the values of 5 and 2 so that you get AC=5 and BC=2. Now you can see that there is a missing leg of the triangle and you need to use Pythagorean’s theorem to find this.

Using the triangle pictured you can use as reference. First do 2^2+b^2=5^2 then simplify to 4+b^2=25. Next subtract 4 on both sides and get b^2=21. Now that you have that you do the square root of both terms on both sides and get b≈4.58.