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Notes Over 8.1

Notes Over 8.1. Solving Oblique Triangles. To solve an oblique triangle , you need to be given one side, and at least two other parts (sides or angles). 4 cases for oblique triangles. 1. Two angles and any side (AAS or ASA). C. 2. Two sides and an angle opposite one of them (SSA). a. b.

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Notes Over 8.1

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  1. Notes Over 8.1 Solving Oblique Triangles To solve an oblique triangle , you need to be given one side, and at least two other parts (sides or angles). 4 cases for oblique triangles 1. Two angles and any side (AAS or ASA) C 2. Two sides and an angle opposite one of them (SSA) a b 3. Three sides (SSS) A B 4. Two sides and their included angle (SAS) c The first two cases use Law of Sines, the last two will use the Law of Cosines.

  2. Notes Over 8.1 Law of Sines If ABC is a triangle with sides a, b, c, then according to the law of sines, or

  3. Notes Over 8.1 The AAS or ASA Case Solve ∆ABC Find:

  4. Notes Over 8.1 The AAS or ASA Case Solve ∆ABC Find:

  5. Notes Over 8.1 The Ambiguous Case (SSA) Consider a triangle where you are given a, b, and A A is acute If the height of the triangle h were equal to a, then it would be a right triangle. a b a a a h a A If a < h, then there would be no triangle. If a > b, then there would be one triangle. If h < a < b, then there would be two triangles.

  6. Notes Over 8.1 The SSA Case – One Triangle Solve ∆ABC Since a > c, one triangle. Find:

  7. Notes Over 8.1 The SSA Case – Two Triangles Solve ∆ABC Find h. Since a < h, no triangle.

  8. Notes Over 8.1 The SSA Case – Two Triangles Solve ∆ABC Find h. Since h < a < b, two triangles

  9. Notes Over 8.1 Area of an Oblique Triangle For any triangle, given two sides and the included angle • Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102o.

  10. Notes Over 8.1 Pg. 588, 8.1 #1-18 all

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