Problems in 3D OCR Stage 9.

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Presentation transcript:

Problems in 3D OCR Stage 9

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

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

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

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

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-1 0.5 = 26.565…º O H Angle GBC = 26. 6º A Consider Triangle GBC

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

A AG² = AC² + CG² AC² = 4² + 9.43² 9.43cm AC² = 104.9249 Calculate AG AG² = AC² + CG² AC² = 4² + 9.43² 9.43cm AC² = 104.9249 AC = √104.9249 AC = 10.2432…cm AC = 10.2 cm 4cm

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

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) = 67.014…º H O Angle AGC = 67.0º A

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

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