Question

To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the shoreline, and that a = 2.72 miles and b = 3.36 miles. Round your answer to two decimal places.)

Answer 1

1) Since we have

a= 2.72

b= 3.36

The best way to find c, (AB) is using the Law of Cosines, that is described by this formula

c² = a² +b² - 2abcos(C)

c² = (2.72)² + (3.36)² -2(2.72)(3.36) cos (40.3)

c² =7.3984 + 11.2896 -2(9.1392) (0.76)

c² =18.688 -13.88064

c² =4.7476

c=√4.7476

c=2.17891

c≅2.18

Note the side we want to find, is the side that we have to plug the cosine.

2) So the answer is c = 2.18 miles