The figure shows the location of 3 points around a lake. the length of the lake, bc, is also shown. (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 8 miles. the length bc of the triangle is labeled as 6 miles. this length bc is also the length of an irregular gray shaded shape. which of the following options is closest to the distance (in miles) between points a and b? 2.24 miles 2.65 miles 3.74 miles 5.29 miles

a right triangle with right angle at B

AC = 8 mi

BC = 6 mi

AB

The Pythagorean theorem tells you

... AC² = AB² + BC²

... 8² = AB² + 6²

... AB² = 64 -36

... AB = √28 ≈ 5.29 . . . . miles

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

c) yes, because of asa or aas