Transcript Problemsin3D

Problems in 3D
OCR Stage 9
What you should know
• Pythagoras’ Theorem
• Trigonometry in right-angled triangles
• Labelling of sides & angles in triangles
H
C
Cuboid E
G
Calculate AC
F
4cm
D 8cm
A
5cm
A
B 5cm
Consider Triangle ABC
8cm
B
C
C
Calculate AC
AC² = 5² + 8²
AC² = 25 + 64
Pythagoras says
8cm
AC² = 89
AC2 = AB2 + BC2
AC = √89
A
AC = 9.433…cm
AC = 9.43cm
5cm
B
Calculate Angle GBC
H
G
E
F
4cm
D
A
C
8cm
5cm
B
SOH CAH TOA
G
Tan angle GBC = 4 / 8 = 0.5
Tan-1 0.5 = 26.565…º
Angle GBC = 26. 6º
B
O
H
8cm
4cm
A
C
Consider Triangle GBC
Calculate Angle GC
H
G
E
F
4cm
D
9.43cm
A
C
8cm
5cm
B
SOH CAH TOA
G
Tan angle AGC = 9.43 / 4
Tan-1 (9.43 ÷ 4) = 67.014…º
Angle AGC = 67.0º
O
H
9.43cm
A
9.43cm
A 4cm
4cm
C
Wedge
A
Angle DBF?
DF?
E
D
C
Can make calculations as in a Cuboid
Isolate & sketch required triangle
B
F