4400 Higher June 2006 Paper 3 Q18

EdexcelHigherOld spec5 marksBasic Trigonometry

Side view of a lorry carrying a rectangular box ABCD; a rope from P on the flat surface goes up to D, over the box, and down from C to Q; DP = 2.3 m, angle APD = 62 degrees, angle BQC = 74 degrees

Diagram NOT accurately drawn

The diagram shows a side view of a rectangular box \(ABCD\) on a lorry.
The box is held down on the horizontal flat surface of the lorry by a rope.
The rope passes over the box and is tied at two points, \(P\) and \(Q\), on the flat surface.

\(DP = 2.3\) m.
Angle \(APD = 62^\circ\).
Angle \(BQC = 74^\circ\).

Calculate the length of \(BQ\).
Give your answer correct to 3 significant figures.

(5)

Mark scheme

Scheme	Marks
\(2.3\sin 62^\circ\)	M1
2.030…	A1
\(\tan 74^\circ = \dfrac{\text{“}2.030\text{”}}{BQ}\) or \(\tan 16^\circ = \dfrac{BQ}{\text{“}2.030\text{”}}\)	M1
\(BQ = \dfrac{\text{“}2.030\text{”}}{\tan 74^\circ}\) or \(BQ = \text{“}2.030\text{”}\tan 16^\circ\)	M1
0.582	A1
	(5)
	(5 marks)

Notes

A1: At least 3 sf May be implied by correct final answer

A1: for 0.582 or better (0.582316…)
Award full marks for 0.58 if all preceding M marks scored
ft from “2.030”
(ft from \(AD = 2 \to 0.5734\ldots\))