4MA0 Higher January 2014 Paper 3R Q17

EdexcelHigherOld spec4 marksBasic Trigonometry Pythagoras

Triangle ABC with D on AB and CD perpendicular to AB; AC = 8.3 cm, AD = 4.7 cm, BD = 7.5 cm

Diagram NOT accurately drawn

The diagram shows triangle \(ABC\).
\(D\) is the point on \(AB\), such that \(CD\) is perpendicular to \(AB\).
\(AC = 8.3\) cm.
\(AD = 4.7\) cm.
\(BD = 7.5\) cm.

Calculate the size of angle \(ABC\).
Give your answer correct to 1 decimal place.

(4)

Mark scheme

Scheme	Marks
\((CD^2 =)\; \sqrt{8.3^2 - 4.7^2}\) or \(\sqrt{68.89 - 22.09}\) or \(\sqrt{46.8}\)	M1
(CD = ) 6.841…	A1
\(\tan \angle ABC = \dfrac{\text{“}6.84\text{”}}{7.5}\) or \(\tan \angle ABC = 0.912\)	M1
42.4	A1
	(4)
	(4 marks)

Notes

A1: for value which rounds to 6.8 (6.84105…)

M1: dep on first M1

A1: for awrt 42.4 (42.3692…)