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Solving Triangles

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad , Glen Whiffen , John Owen, Robert Haese , Sandra Haese and Mark Bruce Haese and Haese Publications, 2004. Chapter 10 – Section G: The Cosine Rule. Solving Triangles. SSS. SAS. SSA.

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Solving Triangles

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Chapter 10 – Section G: The Cosine Rule Solving Triangles SSS SAS SSA ASA, AAS • To solve a non-right triangle you need at least 3 pieces of information: • 3 sides • 2 sides & the angle between • 2 sides & an angle opposite • 2 angles & 1 side

  3. Cosine Rule SSS a2 = b2 + c2 –2bccosA SAS b2 = a2 + c2 –2accosB c2 = a2 + b2 –2abcosC This is all one term. Solving for a Side

  4. 1) Find, correct to 3 sig figs, the length of BC.

  5. Law of Cosines SSS SAS Solving for an Angle

  6. 2) In triangle ABC, if AB = 7 cm, BC = 8 cm and CA = 5 cm, find the measure of angle BCA.

  7. B 5 m 6 m A C 3) A gardener pegs out a rope, 19 meters long, to form a triangular flower bed as shown in this diagram. Calculate: (a) the size of the angle BAC; (b) the area of the flower bed. Diagram not to scale

  8. Chapter 10 – Section H Continued the ambiguous case…of the Sine Rule

  9. 4) In triangle ABC, find the measure of angle C given that c = 10cm, a = 6cm, and A = 30° Scenario 1

  10. 5) In triangle ABC, find the measure of angle C given that c = 10cm, a = 12cm and A = 30° Scenario 2

  11. 6) In triangle ABC, find the measure of angle C given that c = 10cm, a = 5cm, and A = 30° Scenario 3

  12. 7) In triangle ABC, find the measure of angle C given that c = 10cm, a = 3cm, and A = 30° Scenario 4

  13. Homework • Exercise 10G, pg340 • #1, 2, 3 • Exercise 10H.2, pg343 • #2

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