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 $AE^2$” …