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Cosine Rule(II) – Finding Angles

cosA = b 2 + c 2 – a 2. cosB = a 2 + c 2 – b 2. cosC = a 2 + b 2 – c 2. 2bc. 2ac. 2ab. Cosine Rule(II) – Finding Angles. Rearrange a 2 = b 2 + c 2 – (2bccosA). + 2bccosA -a 2 -a 2 + 2bccosA . 2bccosA = b 2 + c 2 – a 2.  2bc. Similarly.

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Cosine Rule(II) – Finding Angles

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  1. cosA = b2 + c2 – a2 cosB = a2 + c2 – b2 cosC = a2 + b2 – c2 2bc 2ac 2ab Cosine Rule(II) – Finding Angles Rearrange a2 = b2 + c2 – (2bccosA) + 2bccosA -a2 -a2 + 2bccosA 2bccosA = b2 + c2 – a2 2bc Similarly

  2. C 12cm 3cm B A 14cm cosA = b2 + c2 – a2 2bc = 32 + 142 - 122 2 x 3 x 14 = 9 + 196 - 144 84 = 61 84 Example1 Find the size of angle A in the diagram below. ************ angle A = cos-1(61  84) = 43.4°

  3. Q 19cm 13cm R S 20cm cosR = q2 + s2 – r2 2qs = 202 + 192 - 132 = 400 + 361 - 169 2 x 20 x 19 760 = 592 760 Example2 Find the size of angle R in the diagram below. ************ angle R = cos-1(592  760) = 38.8°

  4. Obtuse Angles A B A+B sinA° sinB° 70 110 180 0.342 -0.342 55 125 180 0.574 -0.574 20 160 180 0.940 -0.940 47 133 180 0.682 -0.682 CONCLUSIONS • If B is obtuse then cosB° is negative • If A + B = 180 then cosB° = -cosA°

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