1. Law of Cosines
Section 6.2

2. For any oblique triangle the Law of Cosines is:

3. Example 1
Find the missing parts of triangle ABC if

4. If you use my chart or table it looks like this:

5. Example 2
Solve the following triangle:
When using the Law of Cosines with this type of problem, where the three sides are given, it is important to use the form of the Law of Cosines that begins with the longest side. In this problem, we will use the form that begins with b2.

6. If you will enter the last line into your calculator in the following way, you will find the value of B. In this problem, we will give the answer to the nearest degree.
Once you have the value of B, you can use the Law of Sines to find either A or C. For this example, I will find A.
Now we can find C by subtracting A and B from 180.

7. Now you try one.
Solve the following triangle:
Remember that β is the same as B
First decide which form of the Law of Cosines to use. Click when you have completed making the decision and substituted into the formula.
If this is what you have, it is time to solve for b. Try it and then click to see the answer.
Now we need to solve for one of the angles. I’m going to solve for α which is the same as A.

8. In order to solve for A, we use the Law of Sines
In order to solve for A, we use the Law of Sines. In a Law of Cosines problem, we need to use the Law of Cosines only once. Since we are solving for an angle, I want the sines on top. You set up the next equation then click to see it.
If this is what you have, let’s solve for A. Try it and then click for the solution.
All that we have left is to solve for C. You do it then click to check your answer.

9. I have shown you two examples and we have worked through an example together. You should be able to work any Law of Cosines problem now. The next step is to look at a word problem.
A submarine sights a moving target at a distance of 820 m. A torpedo is fired 9° ahead of the target as shown in the diagram and travels 924 m in a straight line to hit the target. How far has the target moved from the time the torpedo is fired to the time of the hit? Round to the nearest tenth of a meter.
Since this is a Law of Cosines problem, we will use the first of the equations to solve the problem. We will let a be the missing side, b equal 820, c equal 924, and A = 9.

10. You have some problems assigned that you should now work
You have some problems assigned that you should now work. Practice will help you understand the Law of Cosines. Good Luck!