4400 Higher November 2010 Paper 3 Q19

EdexcelHigherOld spec6 marksAdvanced Trigonometry

Triangle ABC with AB = 6 cm, BC = 5 cm and angle ACB = 40 degrees

Diagram NOT accurately drawn

Calculate the area of triangle \(ABC\).
Give your answer correct to 3 significant figures.

(6)

Mark scheme

Scheme	Marks
\(\dfrac{\sin A}{5} = \dfrac{\sin 40}{6}\) oe	M1
\(\sin A = \dfrac{5 \sin 40}{6}\) or 0.535...	M1
\(A\) = 32.3 to 32.4	A1
(B =) 180 − 40 − “32.4” (= 107.6 to 107.7)	M1ft
0.5 × 5 × 6 × sin “107.6” (2 sides & a trapped angle)	M1ft
14.3	A1
	(6)
	(6 marks)

Notes

M1ft: dep on M2.

M1ft: or Height = 5 sin 40 (= 3.21) and base = 6 cos “32.4” + 5 cos 40 (= 8.9)
0.5 × 3.21 × “8.9” (must be a correct calculation for height and base)

A1: awrt 14.3