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GCSE Mathematics

GCSE Mathematics. Pythagoras and Trigonometry. Pythagoras. The theorem of Pythagoras will only work on a right angled triangle a c b The longest side, opposite the right angle is the hypotenuse. Pythagoras. a c b a 2 + b 2 = c 2 Alternatively a 2 = c 2 - b 2

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GCSE Mathematics

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  1. GCSE Mathematics Pythagoras and Trigonometry

  2. Pythagoras • The theorem of Pythagoras will only work on a right angled triangle • a c • b • The longest side, opposite the right angle is the hypotenuse

  3. Pythagoras • a c • b • a2 + b2 = c2 • Alternatively a2 = c2 - b2 • or b2 = c2 -a2

  4. x 7 24 x2 = 72 + 242 x2 = 49 + 576 x2 = 625 x = 25 q 18 11 q2 = 182 - 112 q2 = 324 - 121 q2 = 203 q= 14.24 Examples

  5. Pythagoras • Remember to check that the longest length is opposite the right angle. If it is not, you have used the wrong formula.

  6. Trigonometry • The right angled triangles are labelled according to the angle used • Opp Hyp Adj Hyp • Adj Opp • The hypotenuse is always opposite the right angle. x x

  7. Trigonometry • Opp Hyp • Adj • sin x =Opp cos x = adj tan x = Opp • Hyp Hyp adj x

  8. a b c a =? b = 20 x = 30° sin 30 = a/20 a = 20 x sin 30 a = 20 x 0.5 a = 10 a = ? c = 15 x = 28° tan 28 = a/15 a = 15 x tan 28 a = 7.97 b = 26 c =? x = 72° cos 72 = c/26 c = 26 x cos 72 c = 8.03 Finding a length x

  9. a c b a=30 c = ? x = 25 sin 25 = 30 / c c = 30/ sin 25 c = 70.99 b = 40 c = ? x = 35 cos 35 = 40/c c = 40/cos 35 c = 48.83 a = 20 b = ? x = 68 tan 68 = 20 / b b = 20/tan 68 b = 8.08 Finding a length

  10. a c b a = 15 c = 28 x = ? sin x = 15/28 x = sin -1 (15/28) x = 32.39 b = 25 c = 35 x = ? cos x = 25/35 x = cos -1 (25/35) x = 44.42 a = 38 b = 82 x = ? tan x = (38/82) x = tan -1 (38/82) x = 24.86 Finding An Angle x

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