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Triangles: the Ambiguous Case

Triangles: the Ambiguous Case. Source: Glencoe Adv. Mathematical Concepts Pg 324 #16. By: Rachel Atmadja, 2002. The Ambiguous Case. Find all solutions for the triangle below:. B = 37 a = 32 b = 27. C. 27. 32. 37. B. A. The Ambiguous Case.

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Triangles: the Ambiguous Case

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  1. Triangles: the Ambiguous Case Source: Glencoe Adv. Mathematical Concepts Pg 324 #16 By: Rachel Atmadja, 2002

  2. The Ambiguous Case Find all solutions for the triangle below: B = 37 a = 32 b = 27 C 27 32 37 B A

  3. The Ambiguous Case Find all solutions for the triangle below: B = 37 a = 32 b = 27 The ‘magic’ number: 32(sin 37 )= 19.3 C 27 32 37 B A

  4. The Ambiguous Case Find all solutions for the triangle below: B = 37 a = 32 b = 27 The ‘magic’ number: 32(sin 37 )= 19.3 19.3 < 27 < 32 C 27 32 37 B A

  5. The Ambiguous Case Find all solutions for the triangle below: B = 37 a = 32 b = 27 The ‘magic’ number: 32(sin 37 )= 19.3 19.3 < 27 < 32 Therefore, there are 2 solutions C 27 32 37 B A

  6. The Ambiguous Case Find all solutions for the triangle below: Use law of Sines to find A: B = 37 a = 32 b = 27 Sin 37 Sin A 27 32 C = 27 27 32 37 B A

  7. The Ambiguous Case Find all solutions for the triangle below: Use law of Sines to find A: B = 37 a = 32 b = 27 Sin 37 Sin A 27 32 A = 45.5 C = 27 27 32 37 B 45.5 A

  8. The Ambiguous Case Find all solutions for the triangle below: Now find C: B = 37 a = 32 b = 27 Sin 37 Sin A 27 32 A = 45.5 C = 180 – 37 – 45.5 = 97.5 C = 27 32 27 37 B 45.5 A

  9. The Ambiguous Case Find all solutions for the triangle below: Now use the Law of Sines to find side c B = 37 a = 32 b = 27 Sin 37 Sin A Sin 97.5 27 32 c A = 45.5 C = 97.5 C = = 27 32 27 37 B 45.5 A

  10. The Ambiguous Case Find all solutions for the triangle below: Now use the Law of Sines to find side c B = 37 a = 32 b = 27 Sin 37 Sin A Sin 97.5 27 32 c A = 45.5 C = 97.5 c = 44.5 C = = 27 32 27 37 B 45.5 A

  11. The Ambiguous Case Find all solutions for the triangle below: Now to find the 2nd set of solution, let’s being by finding A2: B = 37 a = 32 b = 27 A = 45.5 C = 97.5 c = 44.5 C 27 32 27 37 B 45.5 A A

  12. The Ambiguous Case Find all solutions for the triangle below: Notice that A and A2 are supplementary angles. To find A2, simply subtract A from 180 B = 37 a = 32 b = 27 A = 45.5 A2 = 134.5 C = 97.5 c = 44.5 C 27 32 27 37 B 45.5 A A

  13. The Ambiguous Case Find all solutions for the triangle below: Now find C2. You can find C2 simply by subtracting angles B and A2 from 180. B = 37 a = 32 b = 27 A = 45.5 A2 = 134.5 C = 97.5 C2 = 8.5 c = 44.5 C 27 32 27 37 B 45.5 A A

  14. The Ambiguous Case Find all solutions for the triangle below: Use the Law of Sines to find side c2: B = 37 a = 32 b = 27 A = 45.5 A2 = 134.5 C = 97.5 C2 = 8.5 c = 44.5 C 27 32 27 37 B 45.5 A A

  15. The Ambiguous Case Find all solutions for the triangle below: Use the Law of Sines to find side c2: B = 37 a = 32 b = 27 Sin 37 Sin 8.5 27 c2 A = 45.5 A2 = 134.5 C = 97.5 C2 = 8.5 c = 44.5 c2 = 6.6 C = 27 32 27 37 B 45.5 A A

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