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Triangles and Angles: Solving Problems with the Sine Rule

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Understand how to solve triangles using SSS, SAS, SSA, ASA, AAS with the Sine Rule. Practice applying the rule to find sides and angles accurately.

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Triangles and Angles: Solving Problems with the Sine Rule

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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 H: The Sine 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. C a b B A c Sine Rule SSA ASA, AAS

  4. 1) Find the length of AC.

  5. 2) Find the length of AB.

  6. A 23º C B 15 cm 3) In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and angle ACB is 23°. Find: (a)the size of angle CAB; (b) the length of AB. • Diagram not to scale

  7. 4) A farmer wants to construct a new fence across a field. The plan is shown below. The new fence is indicated by a dotted line. Calculate the length of the fence. 75° 40° 410 m Diagram not to scale

  8. 5)The figure shows a triangular area in a park surrounded by the paths AB, BC and CA, where AB = 400 m. (a) Find the length of AC using the above information. Diana goes along these three paths in the park at an average speed of 1.8 m/s. (b)Given that BC = 788m, calculate how many minutes she takes to walk once around the park.

  9. 6) In triangle ABC, AC = 5, BC = 7, A = 48°, as shown in the diagram Find the measure of angle ABCgiving your answer correct to the nearest degree. C 7 5 48° A B diagram not to scale

  10. 7) The diagram below shows triangle PQR. The length of [PQ] is 7 cm, the length of [PR] is 10 cm, and PQR is 75°. • (a) Find PRQ • (b) Find the area of triangle PQR diagram not to scale

  11. Homework • Worksheet • #1abef • #2a • #3ace • Pg 341 – H.1 2abc

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