1. Law of Cosines

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

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

5. If you use a chart or table it looks like this:

6. Example 2
Solve the following triangle:
In any triangle, the longest side is opposite the largest angle.

9. Solve the following triangle:

10. Now we need to solve for one of the angles. We are going to solve for A.
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.

11. All that we have left is to solve for C.

12. A submarine sights a moving target at a distance of 820 m
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.

13. c a A b
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.

15. Heron’s Formula