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

Solving Triangles Chapter 10 – Section H: The Sine Rule 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 SSS SAS SSA ASA, AAS

Sine Rule SSA A C B a b c ASA, AAS

1) Find the length of AC.

2) Find the length of AB. Math 3 textbook example 14, pg255

3) In the diagram, triangle ABC is isosceles 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 B 23º 15 cm Studies, May 1999, paper 1, question 19 Diagram not to scale

4) A farmer wants to construct a new fence across a field 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 Studies, May 2005, paper 2, question 2 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.

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. A B C 5 7 48° SL, Nov 2002, paper 1, question 2 diagram not to scale

(b) Find the area of triangle PQR 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 SL, May 2008, paper 2, timezone 1, question 2 diagram not to scale

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