AI generatedGeometry and measuresGCSE Higher

Pythagoras in three dimensions

Identify successive right-angled triangles.

  • Identify the right triangle containing the required line or angle.
  • You may first need a face diagonal using Pythagoras.
  • Keep exact values or full calculator accuracy until the final answer.

Example 1

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed4 cm3 cm5 cmACGDiagram not to scale
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.

Example 2

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed5 cm3 cm6 cmACGDiagram not to scale
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.

Your turn

Question 1

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed6 cm3 cm7 cmACGDiagram not to scale
Check answer
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.
Question 2

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed7 cm3 cm8 cmACGDiagram not to scale
Check answer
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.
Question 3

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed8 cm3 cm9 cmACGDiagram not to scale
Check answer
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.
Question 4

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed9 cm3 cm10 cmACGDiagram not to scale
Check answer
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.
Question 5

Find the space diagonal AG. Give an exact answer.

Cuboid with hidden edges dashed10 cm3 cm5 cmACGDiagram not to scale
Check answer
First use Pythagoras in the horizontal base.Then use right triangle ACG.Take the positive root.
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