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 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 SAS ASA, AAS SSS SSA Chapter 10 – Section G: The Cosine Rule

Cosine Rule a 2 =b 2 + c 2 –2bc cosA b 2 =a 2 + c 2 –2ac cosB c 2 =a 2 + b 2 –2ab cosC This is all one term. SSS SAS Solving for a Side

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

Law of Cosines SSS SAS Solving for an Angle

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

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

Chapter 10 – Section H Continued THE AMBIGUOUS CASE… OF THE SINE RULE

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

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

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

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

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