Question

Raymond has taken a position as the navigator on a speed boat racing team. The team entered a race that starts at Daytona Beach, Florida. The first leg of the race course has them traveling due east for 140 miles. They turn right and travel 160 miles for the second leg of the race. They make another right turn to start the third and final leg of the race, in which they will travel 180 miles back to the starting point at Daytona Beach. What is the measure of the turn between the second and third legs of the race? Round your answer to the nearest degree.

Answer 1

48 degrees

Explanation:

You can calculate the angle between the second and third legs of the race by substituting the three side lengths of the triangle in the Law of Cosines.

Answer 2

Using the rules of cosines, the measure of the turn between the second and third legs of the race is given by


`\cos^(-1)\left( (180^2+160^2-140^2)/(2*180*160) \right)=\cos^(-1)\left( (32,400+26,600-19,600)/(57,600) \right) \\ \\ =\cos^(-1)\left( (39,400)/(57,600) \right)=\cos^(-1)(0.6840)\approx47^o`