4MA0 Higher June 2014 Paper 3 Q5

EdexcelHigherOld spec3 marksBasic Trigonometry

Right-angled triangle PQR with the right angle at P; QR = 12.2 cm and angle PRQ = 38°

Diagram NOT accurately drawn

Calculate the length of PQ.
Give your answer correct to 3 significant figures.

(3)

Mark scheme

Scheme	Marks
\(\sin 38 = \dfrac{PQ}{12.2}\) or \(\cos(90 - 38) = \dfrac{PQ}{12.2}\) oe	M1
(“PQ” =) 12.2 × sin 38 or 12.2cos(90 – 38) oe	M1
7.51	A1
	(3 marks)

Notes

A1: awrt 7.51

Alternatively: M1 for 12.2cos38 (9.61...) and \(12.2^2 - \text{“}9.61\text{”}^2\) (= 56.4..); M1 for \(\sqrt{\text{“}56.4\text{”}}\)

or: M1 for a correct statement of sine rule eg \(\dfrac{PQ}{\sin 38} = \dfrac{12.2}{\sin 90}\); M1 for a correct expression for PQ eg \((PQ) = \dfrac{12.2\sin 38}{\sin 90}\)