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The Cosine Rule Theory in a Nutshell • Used to calculate angles & lengths in non-right angled triangles • Formula given in National 5 exam • If calculating a length (a) - requires 2 sides (b & c) and the angle in-between (A) • If calculating an angle (A) – requires all 3 sides (a, b & c) To calculate a length use: A 𝑎𝑎2 = 𝑏𝑏 2 + 𝑐𝑐 2 − 2𝑏𝑏𝑏𝑏 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (Note – b & c is either side of the angle A) c b To calculate an angle use: 𝑏𝑏 2 + 𝑐𝑐 2 − 𝑎𝑎2 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 2𝑏𝑏𝑏𝑏 B c a (Note – b & c is either side of the angle A) Example One – Finding a length 9 cm 𝑥𝑥 28° 12 cm 2 2 2 𝑥𝑥 = 9 + 12 − 2 × 9 × 12 × cos 28 𝑥𝑥 2 = 34.28332 𝑥𝑥 = √34.28332 𝑥𝑥 = 5.9 𝑐𝑐𝑐𝑐 (𝑡𝑡𝑡𝑡 1 𝑑𝑑. 𝑝𝑝. ) www.national5maths.co.uk 2015 Example Two – Finding an angle 21 cm 28 cm 33 cm 𝑐𝑐𝑜𝑜𝑜𝑜 𝑦𝑦 = 𝑦𝑦 282 + 332 − 212 2 × 28 × 33 𝑦𝑦 = 𝑐𝑐𝑐𝑐𝑐𝑐 −1 (0.774891) 𝑦𝑦 = 39.2° (1 𝑑𝑑. 𝑝𝑝. )