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Trigonometry: Section 5.6 The Law of Sines

Trigonometry: Section 5.6 The Law of Sines. Objectives of this Section Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems. All angles are acute. Two acute angles, one obtuse angle. If none of the angles of a triangle is a right angle, the triangle is called oblique.

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Trigonometry: Section 5.6 The Law of Sines

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  1. Trigonometry: Section 5.6The Law of Sines • Objectives of this Section • Solve SAA or ASA Triangles • Solve SSA Triangles • Solve Applied Problems

  2. All angles are acute Two acute angles, one obtuse angle If none of the angles of a triangle is a right angle, the triangle is called oblique. To solve an oblique triangle means to find the lengths of its sides and the measurements of its angles.

  3. FOUR CASES CASE 1: One side and two angles are known (SAA or ASA). CASE 2: Two sides and the angle opposite one of them are known (SSA). CASE 3: Two sides and the included angle are known (SAS). CASE 4: Three sides are known (SSS).

  4. The Law of Sines is used to solve triangles in which Case 1 or 2 holds. The Law of Sines is used to solve SAA, ASA or SSA triangles. Law of Sines

  5. c b 5

  6. b 12 a

  7. Area of Triangles (2 cases) • If 2 sides are known (SAS): • K = ½ bc Sin A (included angle) • K = ½ ac Sin B (included angle) • K = ½ ab Sin C (included angle)

  8. Area of Triangles (2 cases – cont.) • If 2 angles are known: • K = ½ a2Sin B Sin C Sin A • K = ½ b2Sin A Sin C Sin B • K = ½ c2Sin A Sin B Sin C

  9. Ex. 2: Find the area if c = 16.5, b = 21.2, A = 25 °

  10. Ex. 3: Find the area if j = 45.7, K = 111.1°, L = 27.3°

  11. Assignment • Section 5-4 • #1-8 from projector

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