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7.6 Law of Sines

7.6 Law of Sines. Objective. Use the Law of Sines to solve triangles and problems. A. c. b. B. C. a. Law of Sines. In trigonometry, we can use the Law of Sines to find missing parts of triangles that are not right triangles.

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7.6 Law of Sines

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  1. 7.6 Law of Sines

  2. Objective • Use the Law of Sines to solve triangles and problems

  3. A c b B C a Law of Sines • In trigonometry, we can use theLaw of Sines to find missing parts of triangles that are not right triangles. • Law of Sines:In ABC,sin A = sin B = sin C a b c

  4. Example 1a: Find p. Round to the nearest tenth.

  5. Divide each side by sin Answer: Example 1a: Law of Sines Cross products Use a calculator.

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

  7. Answer: Example 1b: Solve for L. Use a calculator.

  8. Answer: Answer: Your Turn: a. Find c. b. Find mTto the nearest degree in RST if r = 12, t = 7, and mT = 76.

  9. Solving a Triangle • The Law of Sines can be used to “solve a triangle,” which means to find the measures of all of the angles and all of the sides of a triangle.

  10. . 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 2a:

  11. Since we know and f, use proportions involving Example 2a: Angle Sum Theorem Add. Subtract 120 from each side.

  12. Example 2a: To find d: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator.

  13. Answer: Example 2a: To find e: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator.

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

  15. Example 2b: Divide each side by 16. Solve for L. Use a calculator. Angle Sum Theorem Substitute. Add. Subtract 116 from each side.

  16. Divide each side by sin Answer: Example 2b: Law of Sines Cross products Use a calculator.

  17. 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: Your Turn:

  18. 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 3:

  19. Since you know the measures of two angles of the triangle, and the length of a side opposite one of the angles you can use the Law of Sines to find the length of the shadow. Example 3:

  20. Divide each side by sin Example 3: Law of Sines Cross products Use a calculator. Answer: The length of the shadow is about 75.9 feet.

  21. Your Turn: 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.

  22. Assignment • Pre-AP Geometry: Pg. 381 #16 – 32 evens, 42 • Geometry: Pg. 381 #16 – 28 evens

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