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 dir
Mathematics
varazdattt
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.)
1 Answer

1. User Answers sqdancefan
Answer:
27 miles
Stepbystep 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.