1. 7.7 Law of Cosines

2. Use the Law of Cosines to solve triangles and problems

3.  Previously, we learned the Law of Sines, which as some theorems can, it does have its limitations. To use the Law of Sines we had to know the measures of two angles and any side (AAS or ASA) OR the measures of two sides and an opposite angle (SSA).  If we don’t have either of these scenarios, but instead we have the measures of two sides and the included angle (SAS) or the measures of all the sides and no angles (SSS), we must use the Law of Cosines. a b

4.  Law of Cosines: In  ABC, a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C B A C c b a

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:

8. Law of Cosines Simplify.

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

11. 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. Since we know the measures of two sides and the included angle, use the Law of Cosines.

12. 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.

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

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

15. 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:

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

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

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

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

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

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

22. 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.

23.  Pre-AP Geometry: Pg. 388 #12 – 38 evens, 40 & 42  Geometry: Pg. 388 #11 & 12, 15 & 16, 19 & 20, 22 & 23, 27 – 30, 42