Problems in 3D

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
Calculate AC
4cm
8cm
5cm
Consider Triangle ABC
4
Calculate AC
AC² 5² 8²
AC² 25 64
Pythagoras says AC2 AB2 BC2
AC² 89
AC v89
AC 9.433cm
AC 9.43cm
5
Calculate Angle GBC
6
SOH CAH TOA
Tan angle GBC 4 / 8 0.5
Tan-1 0.5 26.565º
O
H
Angle GBC 26. 6º
A
Consider Triangle GBC
7
Calculate Angle GC
9.43cm
8
SOH CAH TOA
Tan angle AGC 9.43 / 4
Tan-1 (9.43 4) 67.014º
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