Two automobiles leave a city at the same time and travel along straight highways that differ in direction by 76°.

Question

Two automobiles leave a city at the same time and travel along straight highways that differ in direction by 76°. If their speeds are 45 mi/hr and 60 mi/hr respectively, approximately how far apart (in mi) are the cars at the end of 20 minutes? (Round your answer to the nearest whole number.)

__________mi

Answer 1

Distance travelled by the first car in 20 min is (45 mi/hr)(1/3 hr) = 15 mi

Distance travelled by the second car in 20 min is (60 mi/hr)(1/3 hr) = 20 mi

Let x = distance between the cars after 20 min

By the Law of Cosines, x² = 15² + 20² - 2(15)(20)cos76°

Solve for x.

Answer 2

For these types of problems, it is best to draw a diagram. We can create a triangle using the two directions of the two cars and connect their vectors. When we label our drawing, we should notice we have two side with the included angle (SAS). Thus, we now know we can apply the Law of Cosines. Lastly, we substituted the values we know into the formula for Law of Cosines and calculate for the missing side, c.

I don’t like doing problems with students. I prefer to do the problems with students. In these types of question format, I discuss the steps needed to get to the answer. Many times, it is about the initial steps to create the formula and not all the other calculations. If you do want to work out the problem with me, we can set up a tutoring session. Hope this helps you!