AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Expert: Abe Mantell Date: 5/23/2008 Subject: sine and cosine word problem
Question Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 22mph in a direction 350 degrees. The second sails at 29mph in a direction 220 degrees. Assuming that both boats maintain speed and heading, after 5 hours, how far apart are the boats?
Answer After 5 hrs, the distance they have traveled is:
The 22 MPH boat: 110 miles
The 29 MPH boat: 145 miles
They are offset by an angle of 130 degrees.
Using the Law of Cosines...
Let x=the distance between them, so
x^2 = 110^2 + 145^2 - 2(110)(145)cos(130 degrees)
x^2 = 53629.92475
Thus, x is about 231.58 miles.
