Problems in 3D

OCR Stage 9

What you should know

• Pythagoras’ Theorem

• Trigonometry in right-angled triangles

• Labelling of sides & angles in triangles

Cuboid

A

H

E

D

C

B

G

FCalculate AC

Consider Triangle ABC

5cm

4cm

8cmA B

C

8cm

5cm

Calculate AC

A B

C

8cm

5cm

Pythagoras says

AC2 = AB2 + BC2

AC² = 5² + 8²

AC² = 25 + 64

AC² = 89

AC = √89

AC = 9.433…cm

AC = 9.43cm

A

H

E

D

C

B

G

F

5cm

4cm

8cm

Calculate Angle GBC

Consider Triangle GBC

C

G

B8cm

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

A

H

E

D

C

B

G

F

5cm

4cm

8cm

Calculate Angle GC

9.43cm

A

GC

9.43cm

4cm

A

G

C9.43cm

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

Wedge

FE

D C

BA

Can make calculations as in a Cuboid

Isolate & sketch required triangle

DF?Angle DBF?