©G Dear2008 – Not to be sold/Free to use General Mathematic (HSC) Further Trigonometry Area Formula Stage 6 - Year 12 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use

Find the Area using Sine (1/4) b a Web C 1 2 Area = ab x Sin C To use the Area Rule we need … two sides and … the angle between them.

Find the Area using Sine (2/4) Find Area of a Doritos. 1 2 Area = ab x Sin C 1 2 = x 4 x 4 x Sin 60o ≈ 6.9 cm2 60o

Find the Area using Sine (3/4) Find Area of a Doritos. 1 2 Area = bh 1 2 = x 4 x 3.6 = 7.2 cm2

Find the Area using Sine (4/4) Find Area of a Doritos. Error!!! Why the Difference? Error!!! 1 2 Area = ab x Sin C a = 4, b = 4, c = 60o Lower Limit = 0.5 x 3.95 x 3.95 x Sin 59.5o ≈ 6.7 Upper Limit = 0.5 x 4.05 x 4.05 x Sin 60.5o ≈ 7.1 1 2 Area = bh b = 4, h = 3.6 Lower Limit = 0.5 x 3.95 x 3.55 = 7.0 Upper Limit = 0.5 x 4.05 x 3.65 = 7.4 The error in both calculations overlap so both answers could be correct within the error limits.