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” …