Learning pack · IGCSE handout

Trigonometry in Three Dimensions

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). 3D trigonometry combines Pythagoras in space with right-angled trig in carefully chosen planes.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

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Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 📖 Full summary

Files: 25_trigonometry_in_three_dimensions_handout.pdf · 25_trigonometry_in_three_dimensions_handout_answers.pdf

Full topic summary

3D trigonometry combines Pythagoras in space with right-angled trig in carefully chosen planes.

Key learning points

Sketch the triangle that actually contains the angle or length you need.
Space diagonal of a cuboid: $\sqrt{l^2+w^2+h^2}$ .
Angle between a line and a plane: drop a perpendicular to the plane.

Worked example 1 — Space diagonal

Cuboid $2\times3\times6$ . Space diagonal?

Working

7

$\sqrt{l^2+w^2+h^2}$ .

Worked example 2 — Face diagonal

Base $3\times4$ . Face diagonal?

Working

5

Pythagoras in the face.

Worked example 3 — Angle with base

Method for angle between space diagonal and base?

Working

\tan\theta=\frac{h}{\text{face diagonal}}

Right triangle from height and face diagonal.

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