Two boats...

Question

Two boats leave a dock together, each traveling in a straight line. One boat travels at 33mph and the other at 24 mph. If the angle between their courses measures 63.0°, how far apart are they after 36 minutes?

Answer 1

first we got to find how many hours 36min are

36/60 = 0.6 hours

 

after 0.6 h the first boat has traveled 0.6hx33mph=19.8m

the second boat 0.6hx24mph=14.4m

 

so we have a triangle two sides of which are 19.9m and 14.4 m and the angle between them is 63

use the consine rule

 

c² = a² + b² - 2abcos∂

 

c² =(14.4)² + (19.8)² - 2 (14.4) (19.8) cos63

 

where cos63= 0.453

c² = 207.36 + 392.04 - 258.32

c²=341.081

c=18.47 m

 

so after 36 min the boats will be approx. 18.5 miles appart

Answer 2

First convert miles per hour to miles per minute

33mi/hr =33mi/60min=11mi/20min

24mi/hr=24mi/60min=2mi/5min

 

To find out how far they have traveled in 36min you multiply each fraction times 36min.

11/20 x 36= 19.8mi

2/5 x 36= 14.4 mi

 

You now have two sides and an angle and you are trying to find the third side.

Use the law of cosines

a²=b²+c²-2bc * cosA

a²= (19.8)²+(14.4)²-2(19.8)(14.4)cos(63)

a²= 392.04+207.36-570.24cos(63)

Take the square root of both sides (because you still have a²)

a=5.36