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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 H: The Sine Rule Solving Triangles • To solve a non-right triangle you need at least 3 pieces of information: – 3 sides SSS – 2 sides & the angle between – 2 sides & an angle opposite – 2 angles & 1 side ASA, AAS SAS SSA Sine Rule a b c sin A sin B sin C SSA ASA, AAS C a b A c B 1) Find the length of AC. 2) Find the length of AB. 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. A C 23º 15 cm Diagram not to scale B 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 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. diagram not to scale A 400 m 30º B C 6) In triangle ABC, AC = 5, BC = 7, A = 48°, as shown in the diagram Find the measure of angle ABC giving your answer correct to the nearest degree. C 7 5 A 48° diagram not to scale B 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 Homework • Worksheet –#1abef –#2a –#3ace • Pg 341 – H.1 2abc