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 C A B H G E Calculate AC F D A C B Consider Triangle ABC 4cm

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

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

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

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

8. A AG² = AC² + CG² AC² = 4² + 9.43² 9.43cm AC² = 104.9249
Calculate AG
AG² = AC² + CG²
AC² = 4² ²
9.43cm
AC² =
AC = √
AC = …cm
AC = 10.2 cm
4cm

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

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

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

12. Homework: Exercise 15E.1 Page 461 # 1 to 6