1. Law of Sines and Law of Cosines Examples / Practice

2. Example 6-1a Find p. Round to the nearest tenth.

3. Example 6-1c Law of Sines Cross products Divide each side by 7. to the nearest degree in,

4. a. Find c. b. Find m  T to the nearest degree in  RST if r = 12, t = 7, and m  T = 76. Example 6-1e Answer:

5. Example 6-2a We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find. Round angle measures to the nearest degree and side measures to the nearest tenth.

6. Example 6-2e We know the measure of two sides and an angle opposite one of the sides. Law of Sines Cross products Round angle measures to the nearest degree and side measures to the nearest tenth.

7. Answer: a. Solve Round angle measures to the nearest degree and side measures to the nearest tenth. b. Round angle measures to the nearest degree and side measures to the nearest tenth. Example 6-2h Answer:

8. Example 6-3a A 46-foot telephone pole tilted at an angle of from the vertical casts a shadow on the ground. Find the length of the shadow to the nearest foot when the angle of elevation to the sun is Draw a diagram Draw Then find the

9. Example 6-3d A 5-foot fishing pole is anchored to the edge of a dock. If the distance from the foot of the pole to the point where the fishing line meets the water is 45 feet, about how much fishing line that is cast out is above the surface of the water? Answer: About 42 feet of the fishing line that is cast out is above the surface of the water.

10. Example 7-1a Use the Law of Cosines since the measures of two sides and the included angle are known.

11. Example 7-1b Simplify. Take the square root of each side. Law of Cosines Use a calculator. Answer:

12. Example 7-1c Answer:

13. Example 7-2a Law of Cosines Simplify.

14. Example 7-2b Solve for L. Use a calculator. Subtract 754 from each side. Divide each side by –270. Answer:

15. Example 7-2c Answer:

16. Example 7-3a 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.

17. Example 7-3b 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.

18. Example 7-3c Cross products Divide each side by 46.9. Law of Sines Take the inverse of each side. Use a calculator.

19. Example 7-3d Use the Angle Sum Theorem to find Angle Sum Theorem Subtract 168 from each side. Answer:

20. Example 7-3e 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:

21. Since is an isosceles triangle, Example 7-4a AIRCRAFT From the diagram of the plane shown, determine the approximate exterior perimeter of each wing. Round to the nearest tenth meter.

22. Example 7-4b Cross products Law of Sines Simplify. Divide each side by sin. Use the Law of Sines to find KJ.

23. Example 7-4c Use the Law of Sines to find. Cross products Law of Sines Solve for H. Divide each side by 9. Use a calculator.

24. Example 7-4d Use the Angle Sum Theorem to find Subtract 95 from each side. Angle Sum Theorem

25. Example 7-4e Use the Law of Sines to find HK. Cross products Law of Sines Use a calculator. Divide each side by sin

26. Example 7-4f Answer: The perimeter is about or about 67.1 meters. The perimeter of the wing is equal to

27. Example 7-4g 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.