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Geometry IB Date : 4/22/2014 Question: How do we measure the immeasurable ? SWBAT use the Law of Sines to solve

Geometry IB Date : 4/22/2014 Question: How do we measure the immeasurable ? SWBAT use the Law of Sines to solve triangles and problems Agenda Bell Ringer: Put up Assigned problems Go over 8.2/8.3 Quiz HW Requests – ws Angle of Elevation and Depression 8.5

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Geometry IB Date : 4/22/2014 Question: How do we measure the immeasurable ? SWBAT use the Law of Sines to solve

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  1. Geometry IB Date: 4/22/2014 Question: How do we measure the immeasurable? SWBATuse the Law of Sines to solve triangles and problems Agenda Bell Ringer: Put up Assigned problems Go over 8.2/8.3 Quiz HW Requests – ws Angle of Elevation and Depression 8.5 pg 577 #8-11, 17-21, 23, 24, 38 HW: WS old textbook on Law of Sines Announcements:
  2. 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
  3. The Law of Sines! L.T.: Be able to use the Law of Sines to find unknowns in triangles! Quick Review: What does Soh-Cah-Toa stand for? What kind of triangles do we use this for? right triangles What if it’s not a right triangle? GASP!! What do we do then??
  4. B c a A C b The Law of Sines: Note: capital letters always stand for __________! lower-case letters always stand for ________! Use the Law of Sines ONLY when: you DON’T have a right triangle AND you know an angle and its opposite side angles sides
  5. Example 1 You are given a triangle, ABC, with angle A = 70°, angle B = 80° and side a = 12 cm. Find the measures of angle C and sides b and c. * In this section, angles are named with capital letters and the side opposite an angle is named with the same lower case letter .*
  6. B 80° a = 12 c 70° A C b Example 1 (con’t) The angles in a ∆ total 180°, so angle C = 30°. Set up the Law of Sines to find side b: =
  7. B 80° a = 12 c 70° 30° A C b = 12.6 Example 1 (con’t) Set up the Law of Sines to find side c: =
  8. B 80° a = 12 c = 6.4 70° 30° A C b = 12.6 Example 1 (solution) Angle C = 30° Side b = 12.6 cm Side c = 6.4 cm Note: We used the given values of A and a in both calculations. Your answer is more accurate if you do not used rounded values in calculations.
  9. Example 1a: Find p. Round to the nearest tenth.
  10. Divide each side by sin Answer: Example 1a: Law of Sines Cross products Use a calculator.
  11. to the nearest degree in , Example 1b: Law of Sines Cross products Divide each side by 7.
  12. Answer: Example 1b: Solve for L. Use a calculator.
  13. 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.
  14. 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.
  15. . 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:
  16. Since we know and f, use proportions involving Example 2a: Angle Sum Theorem Add. Subtract 120 from each side.
  17. Example 2a: To find d: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator.
  18. Answer: Example 2a: To find e: Law of Sines Substitute. Cross products Divide each side by sin 8°. Use a calculator.
  19. 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
  20. Example 2b: Divide each side by 16. Solve for L. Use a calculator. Angle Sum Theorem Substitute. Add. Subtract 116 from each side.
  21. Divide each side by sin Answer: Example 2b: Law of Sines Cross products Use a calculator.
  22. 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:
  23. 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:
  24. 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:
  25. 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.
  26. 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.
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