Optional extension: Space diagonals, tangents and combined lengths
Example 1
A cuboid has dimensions 6cm,18cm and 27cm. Find its space diagonal.
CuboidDiagram not to scaleShow worked answer
Answer: 33
- Use Pythagoras twice: d2=62+182+272=1089.
- Thus d=33cm.
Example 2
A circle has centre O and radius 60cm. P is 68cm from O. PT is tangent to the circle at T. Find PT.
Radius and tangentDiagram not to scaleShow worked answer
Answer: 32
- Radius OT is perpendicular to tangent PT.
- Thus PT2=OP2−OT2=682−602, giving PT=32cm.
Example 3
A cuboid has dimensions 4cm,12cm and 18cm. Find its space diagonal.
CuboidDiagram not to scaleShow worked answer
Answer: 22
- Use Pythagoras twice: d2=42+122+182=484.
- Thus d=22cm.