Step by Step

Let's take a closer look at each of the steps for solving a problem using the Law of Cosines. Suppose you are given the following information about a triangle:

m∠A = 143°
b = 17
c = 22

How can you use the Law of Cosines to find the measurements of other parts of the triangle. Study the step on each slide carefully to make sure you understand how to perform each part of a solution that uses the Law of Cosines. Answer any questions in your notebook before clicking the button to check your work.

Step 1

First, determine the information that is given in the problem. This problem includes the measure of angle A and the length of sides b and c. We can use this information to find the length of side a.

Step 2

Next, draw a picture of this triangle, since one has not been provided.

Triangle

Step 3

Triangle

The next step is very important: Determine which formula of the Law of Cosines will help you solve this problem. Think about the information that you are given to decide which formula to use.

Since we are given b, c and angle A, we can use the following formula to solve for side a. a² = b² + c² - 2bc cos(A)

Step 4

Triangle

Finally, substitute your known values into the formula from Step 3, and solve for the missing side a.

a² = b² + c² - 2bc cos(A)
a² = 17² + 22² - 2(17)(22)cos(143°)
a² = 289 + 484 - 748cos(143°)
a² = 289 + 484 - (-597.4)

Hint: Remember that "minus a negative" is the same as "plus a positive".

a² = 1370.4
a ≈ 37

What does each step look like?

Step 1

Step 2

Step 3

Step 4