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1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

1316 Trigonometry Law of Sines Chapter 7 Sections 1&2. C. b. a. h. A. B. c. There is group of formulas that work for most triangles. Requirements when using the Law of Sines:. You must be given two angles and any side: AAS or ASA. OR. Two sides and an angle opposite one of them: SSA.

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1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

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  1. 1316 TrigonometryLaw of SinesChapter 7 Sections 1&2

  2. C b a h A B c There is group of formulas that work for most triangles.

  3. Requirements when using the Law of Sines: You must be given two angles and any side: AAS or ASA OR Two sides and an angle opposite one of them: SSA The Law of Sines does not work for SSS or SAS

  4. Find all sides and angles if C = 102.3°, B = 28.7°, and b = 27.4 feet. C 27.4 ft 102.3° b a A 49.0° 28.7° B c

  5. C b a = ? A B c A pole tilts toward the sun at an angle of 8°. If it casts a 22 foot shadow and the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole? 39° 98° 43° shadow = 22 ft

  6. a b a b a a b b When you are given two sides and a non-included angle (SSA) – three possibilities exist You will get no triangle You will get one triangle You will get two triangles

  7. Find all angles if A = 85°, a = 15, and b = 25 ft. C 25 ft b a = 15 ft A 85° B c This does not exist so there is no triangle.

  8. Find all angles if A = 20.5°, a = 12, and b = 31 feet. C 44.3° 31 ft 94.7 ° b a = 12 ft 115.2° 20.5° A 64.8 ° 20.5° B c This happens twice on (0°,180°)

  9. Use the Law of Sines to find B: C 8 6 87° B A With Sine there may be an angle in Quad II that also works so you must check the supplement: This is too large to be a triangle with the 87 given

  10. Use the Law of Sines to find B: C 3.5 4 60° B A Check the supplement: The data makes two triangles since both 81.8 & 98.2 work with 60

  11. Use the Law of Sines to find C: C 100 67° B A 125 No triangle will be formed with these numbers.

  12. Draw a triangle for each and use the Law of Sines to decide how many triangles are formed • B = 47°, b = 4, c = 25 No Triangle • C = 60°, b = 30, c = 50 One Triangle • 3) B = 20°, a = 12, b = 5 Two triangles • 4) B = 37.3°, b = 12.5, c = 20.1 Two triangles • 5) A = 102°, a = 5, c = 12 No triangles

  13. Basic Steps for working with Law of Sines Draw and label a figure Use Law of Sines with the parts you are given When you find an angle (Sin-1) check if the supplement also makes a triangle Find all missing parts that are requested.

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