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

4. Calculate AC A B C 8cm 5cm Pythagoras says AC 2 = AB 2 + BC 2 AC² = 5² + 8² AC² = 25 + 64 AC² = 89 AC = √89 AC = 9.433…cm AC = 9.43cm

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

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

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

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

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