AI generatedGeometry and measuresGCSE Higher

Trigonometry in three dimensions

Identify the right triangle containing the required length or angle.

  • 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 angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed4 cm3 cm5 cmACGDiagram not to scale
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.

Example 2

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed5 cm3 cm6 cmACGDiagram not to scale
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.

Your turn

Question 1

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed6 cm3 cm7 cmACGDiagram not to scale
Check answer
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.
Question 2

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed7 cm3 cm8 cmACGDiagram not to scale
Check answer
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.
Question 3

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed8 cm3 cm9 cmACGDiagram not to scale
Check answer
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.
Question 4

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed9 cm3 cm10 cmACGDiagram not to scale
Check answer
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.
Question 5

Find the angle AG makes with the horizontal base. Give your answer to 1 decimal place.

Cuboid with hidden edges dashed10 cm3 cm5 cmACGDiagram not to scale
Check answer
Find the projection of AG on the base.In triangle ACG, use opposite ÷ adjacent.Use inverse tangent.Keep full calculator accuracy until the end.
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