Question

Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 25 mph in a direction 340°. The second sails at 29 mph in a direction 210°. Assuming that both boats maintain speed and heading, after 5 hours, how far apart are the boats?

A. 157.4 mi
B. 212 mi
C. 175 mi
D. 244.8 mi

Answer 1

9514 1404 393

Answer:

D. 244.8 mi

Explanation:

The law of cosines can be used to find the distance between the boats.

The first boat will have traveled (5 h)×(25 mi/h) = 125 mi. The second boat will have traveled (5 h)×(29 mi/h) = 145 mi. The angle between their travel directions is 340° -210° = 130°.

c² = a² +b² -2ab·cos(C) . . . . . for a=125, b=145, C=130°

c² ≈ 59951.05

c ≈ √59951.05 ≈ 244.8 . . . miles

The boats are about 244.8 miles apart after 5 hours.