4400 Higher June 2005 Paper 3 Q18

EdexcelHigherOld spec6 marksAdvanced Trigonometry

Triangle ABC with BC = 9.4 cm, angle BAC = 123 degrees and angle ABC = 35 degrees

Diagram NOT accurately drawn

\(BC = 9.4\) cm.
Angle \(BAC = 123^\circ\).
Angle \(ABC = 35^\circ\).

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

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

Scheme	Marks
\(\dfrac{9.4}{\sin 123^\circ} = \dfrac{AC}{\sin 35^\circ}\)	M1
\(AC = \dfrac{9.4 \sin 35^\circ}{\sin 123^\circ}\)	M1
6.43	A1
	(3)

Mark scheme (b)

Scheme	Marks
\(\frac{1}{2} \times 9.4 \times \text{“}6.43\text{”} \times \sin x^\circ\) or \(\frac{1}{2} \times AB \times \text{“}6.43\text{”} \times \sin 123^\circ\) or \(\frac{1}{2} \times AB \times 9.4 \times \sin 35^\circ\)	M1 B1
11.3	A1
	(3)
	(6 marks)

Notes

M1: For clear attempt to use “\(\frac{1}{2}ab\sin C\)”

B1: For \(x = 22\) or \(AB = 4.2\) or better (4.1987…) appropriate for their form of \(\frac{1}{2}ab\sin C\)
If M0, award for \(x = 22\) or \(AB = 4.2\) or better (may be shown on diagram)

A1: 11.3 or better (11.3188); ft from (a)