Mathematics 0580 · IGCSE · Pythagoras' theorem and trigonometry in 3D
Pythagoras' theorem and trigonometry in 3D — practice question
The sketch depicts triangle $ABC$ on level ground. $AC=15$ m, $BC=8$ m and $AB=20$ m. $BP$ and $CQ$ are vertical poles with unequal heights. $BP=3$ m and $CQ=4$ m. $AQ$ and $PQ$ are straight wires.
(a)[4]
Show that angle $ACB = 117.5^\circ$, accurate to 1 decimal place.
(b)[2]
Calculate the area enclosed by triangle $ABC$.
(c)[2]
Calculate the distance $AQ$.
(d)[3]
Calculate the angle of elevation of $Q$ as seen from $P$.
(e)[5]
Calculate the angle that this wire makes with the horizontal ground.
Worked solution & mark scheme
This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\cos = \frac{15^2 + 8^2 - 20^2}{2 \times 15 \times 8}$” …