Law of Sines and Law of Cosines Examples / Practice

1. Law of Sines andLaw of Cosines Examples / Practice

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

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

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

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

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

7. 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. Answer: Answer: Example 6-2h

8. 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 Example 6-3a

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

12. Answer: Example 7-1c

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

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

15. Answer: Example 7-2c

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. Example 7-3a Since we know the measures of two sides and the included angle, use the Law of Cosines.

17. 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. Example 7-3b Law of Cosines Take the square root of each side. Use a calculator.

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

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

20. 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: Example 7-3e

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

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

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

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

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

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.