The document discusses the Law of Cosines and how it can be used to solve triangles when two sides and the included angle are known (SAS) or when all three sides are known (SSS). It provides examples of using the Law of Cosines to solve for missing side lengths and angles of triangles. It also discusses using the Law of Sines and Angle Sum Theorem in conjunction with the Law of Cosines to determine values in multi-step triangle problems.

1. Law of Cosines Pg 733

5. Use the Law of Cosines since the measures of two sides and the included angle are known.

6. Simplify. Take the square root of each side. Law of Cosines Use a calculator. Answer:

7. Answer:

8. Law of Cosines Simplify.

9. Solve for L. Use a calculator. Subtract 754 from each side. Divide each side by –270. Answer:

10. Answer:

12. Since we know the measures of two sides and the included angle, use the Law of Cosines. Determine whether the Law of Sines or the Law of Cosines should be used first to solve Then solve Round angle measures to the nearest degree and side measures to the nearest tenth.

13. Take the square root of each side. Use a calculator. Law of Cosines Next, we can find If we decide to find we can use either the Law of Sines or the Law of Cosines to find this value. In this case, we will use the Law of Sines.

14. Cross products Divide each side by 46.9. Law of Sines Take the inverse of each side. Use a calculator.

15. Angle Sum Theorem Subtract 168 from each side. Use the Angle Sum Theorem to find Answer:

16. Determine whether the Law of Sines or the Law of Cosines should be used first to solve Then solve Round angle measures to the nearest degree and side measures to the nearest tenth. Answer:

17. AIRCRAFT From the diagram of the plane shown, determine the approximate exterior perimeter of each wing. Round to the nearest tenth meter. Since is an isosceles triangle,

18. Cross products Law of Sines Simplify. Use the Law of Sines to find KJ. Divide each side by sin .

19. Cross products Law of Sines Solve for H. Divide each side by 9. Use a calculator. Use the Law of Sines to find .

20. Subtract 95 from each side. Angle Sum Theorem Use the Angle Sum Theorem to find

21. Use the Law of Sines to find HK. Cross products Law of Sines Use a calculator. Divide each side by sin

22. Answer: The perimeter is about or about 67.1 meters. The perimeter of the wing is equal to

23. The rear side window of a station wagon has the shape shown in the figure. Find the perimeter of the window if the length of DB is 31 inches. Answer: about 93.5 in.