Topic summary · IGCSE handout

Trigonometry in Three Dimensions summary

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

Open Learning Sheet — Trigonometry in Three Dimensions Download Trigonometry in Three Dimensions answers PDF

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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.

Scaffolded Learning Sheet and answers (PDFs)

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