College Algebra & Trigonometry, 2018a

496 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
11.4 Applications
In the previous sections on applications, we saw situations in which right triangle
trigonometry was used to find distances and angles. In this section, we will use
the Law of Sines and the Law of Cosines to find distances and angles.
Example 1
A car travels along a straight road, heading west for 1 hour, then traveling on
another straight road northwest for a half hour. If the speed of the car was a
constant 50 mph how far is the car from its starting point?
First, let’s draw a diagram:
C
45 ◦ 135 ◦
B
A
In the picture above, we know the angles 45 ◦ and 135 ◦ because of the direction the
car was traveling. The direction northwest cuts exactly halfway between north
and west creating a 45 ◦ angle. On the other side of this 45 ◦ angle is a 135 ◦ angle
which is in the triangle we’ll use to answer the question (triangle ABC).
The length of AB is 50 miles and the length of BC is 25 miles. This comes from
the information about the speed and traveling time given in the problem. So the
triangle we need to answer the question is pictured below:
C
a =25 135 ◦ b =?
B c =50
A