Mathematics 0580 · IGCSE · Pythagoras' theorem and trigonometry in 3D

Pythagoras' theorem and trigonometry in 3D — practice question

For pentagon $ABCDE$, angle $ACB$ is $90^\circ$ and angle $AED$ is $90^\circ$. Triangle $ACD$ is equilateral with side length 12 cm. Also, $DE = BC = 6$ cm.
(a(i))[4]

Calculate the value of angle $BAE$.

(a(ii))[2]

Calculate the length $AB$.

(a(iii))[3]

Calculate the length $AE$.

(a(iv))[4]

Calculate the pentagon's area.

(b(i))[1]

Write down how many planes of symmetry this cuboid has.

(b(ii))[4]

Calculate the angle formed by diagonal $AR$ and plane $BCRQ$.

Worked solution & mark scheme

This 18-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies the correct trigonometric ratios

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