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3D OCR Stage 9: Pythagoras' Theorem, Trigonometry, and Triangle Labeling

Learn the essential concepts of Pythagoras' Theorem, Trigonometry in right-angled triangles, and labeling of sides and angles in triangles. Solve problems in a cuboid and isolate and sketch the required triangle.

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3D OCR Stage 9: Pythagoras' Theorem, Trigonometry, and Triangle Labeling

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  1. Problems in 3D OCR Stage 9

  2. What you should know • Pythagoras’ Theorem • Trigonometry in right-angled triangles • Labelling of sides & angles in triangles

  3. H C G E F D 8cm A C B A B 5cm Cuboid Calculate AC 4cm 8cm 5cm Consider Triangle ABC

  4. C 8cm 5cm A B Calculate AC AC² = 5² + 8² AC² = 25 + 64 Pythagoras says AC2 = AB2 + BC2 AC² = 89 AC = √89 AC = 9.433…cm AC = 9.43cm

  5. H G E F 4cm D A C 8cm 5cm B Calculate Angle GBC

  6. G 4cm B C 8cm SOH CAH TOA Tan angle GBC = 4 / 8 = 0.5 Tan-1 0.5 = 26.565…º O H Angle GBC = 26. 6º A Consider Triangle GBC

  7. H G E F 4cm D A C 8cm 5cm B Calculate Angle GC 9.43cm

  8. A G 4cm 9.43cm A C 9.43cm G C 4cm SOH CAH TOA Tan angle AGC = 9.43 / 4 Tan-1 (9.43 ÷ 4) = 67.014…º H O Angle AGC = 67.0º A

  9. Wedge A B Angle DBF? DF? E F D C Can make calculations as in a Cuboid Isolate & sketch required triangle

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