1. Warm up Notes Preliminary Activity Activity For Fun Area of a Triangle

2. Back 1. The compass bearing for this diagram is A WSB EN C SWD NE 2. The true bearing of A from O in the diagram is A 053 o TB 127 o T C 307 o TD 53 o T 3. A ship sails 57 km from a port A on a bearing of 298 o T. The distance the ship is North of its starting point is A 26.8 kmB 64.6 kmC 107.2 kmD 121.4 km 4. A town X is 58 km East and 113 km South of town Y. The bearing of X from Y is closest to A SEB NEC 063 o TD 153 o T 5. The value of θ is closest to A 36 o 51 ' B 43 o 16 ' C 81 o 6 ' D 99 o 54 ' 6. The value of θ in this triangle is closest to A 40 o 19 ' B 18 o 39 ' C 18 o 40 ' D 28 o

3. Back The formula for the area of a triangle base b, perpendicular height h, is Area = ½bh. Examine the area of a triangle ABC with base AC and perpendicular height h. Area of ΔABC = ½ x base x height = ½ x CA x BX = ½bh...... (1) In ΔBXC, sin C = opp hyp ∴ sin C = h a ∴ h = a sin C......(2) Combining (1) and (2) gives Area = ½b(a sinC) i.e., Area = ½ab sinC i.e., given two sides and the included angle of a triangle, the area is given by Area = ½ab sinC Similarly, the area is given by Area = ½ac sinB andArea = ½bc sinA

4. Back Find the area of the following triangle: a) b) Area = ½absinC = ½ x 14 x 12 x sin57 o = 70.4cm 2 (1 decimal place) Area = ½pr sinQ = ½ x 11 x 8 x sin130 o = 33.7cm 2 (1 decimal place)

5. Back 41.7% 56.3% 75.7% Complete exercise 5-08 Questions 1, 2, 4, 6, 8, 10, 11

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