Answer to Question #1146 in Trigonometry for Javier Rodriguez

Question

Two cars leave the same place at the same time. The first drives in a straight line N 35 Degrees W at 30 miles per hour and the second drives in a straight line N 12 Degrees E at 40 miles per hour. After 1 hour, how far apart are the cars(to the nearest mile)?

Answer 1

The distance between the cars equals to the side of triangle with other two sides of 30 and 40 miles and the


angle between them of (35+12)= 47 degrees.
According the Law of cosines:
C² = a²+b² - 2 ab cos(theta)
C² = 30²+40²-2*30*40*cos(47) = 863.2
C = 29.4 miles.