Mathematics 4024 · O Level · Pythagoras' theorem and trigonometry in 3D
Pythagoras' theorem and trigonometry in 3D — practice question
The building’s four walls make up the faces of cuboid $ABCDEFGH$. Because $T$ is positioned vertically above $C$ and $G$, $\angle ABT = \angle ADT = 90^\circ$. The cuboid is $9\text{ m}$ long, $8\text{ m}$ wide and $5\text{ m}$ high. $TC = 6\text{ m}$.
(a)[2]
Calculate the value of $DT$.
(b)[3]
The roof consists of four triangles, $ABT$, $BCT$, $CDT$ and $DAT$. Calculate the roof’s total surface area.
(c)[2]
Calculate the total volume of the building.
(d)[3]
Calculate the angle of elevation from $H$ to $T$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Pythagoras’ theorem” …