Question

Two boats leave the same port at the same time. One travels at a speed of 28 mi/h in the direction N 50° E, and the other travels at a speed of 26 mi/h in a direction S 70° E (see the figure). How far apart are the two boats after 1 h? (Round your answer to the nearest mile.)

Answer 1

27 miles

Explanation:

The law of cosines can be used to find the distance between the boats. In 1 hour, one has traveled 28 miles, and the other has traveled 26 miles. The angle between their directions of travel is ...

180° -50° -70° = 60°

Then the distance c can be found from ...

c^2 = a^2 +b^2 -2ab·cos(C)

c^2 = 28^2 +26^2 -2·28·26·cos(60°) = 732

c = √732 ≈ 27.055

The boats are 27 miles apart after 1 hour.