Mathematics 4024 · O Level · Pythagoras' theorem and trigonometry in 3D

Pythagoras' theorem and trigonometry in 3D — practice question

The diagram depicts a pyramid with a rectangular base lying horizontally. Vertex $F$ of the pyramid is directly above the centre of the base, $E$. $AB = 6.2\,\text{cm}$ and $BC = 4.3\,\text{cm}$. Each sloping edge of the pyramid measures $9.5\,\text{cm}$.
(a)[4]

Show that the height, $EF$, of the pyramid is $8.72\,\text{cm}$, correct to $3$ significant figures.

(b)[2]

Calculate the volume of the pyramid.

(c)[3]

Calculate angle $AFB$.

(d)[2]

Calculate the angle of elevation of $F$ from the midpoint of $AB$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Begin with $AE^2$

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