4MA0 Higher June 2013 Paper 4 Q22

EdexcelHigherOld spec4 marksAdvanced Trigonometry Pythagoras

22 The diagram shows a triangular prism with a horizontal rectangular base \(ABCD\).
\(AB = 10\) cm. \(BC = 7\) cm.
\(M\) is the midpoint of \(AD\).
The vertex \(T\) is vertically above \(M\).
\(MT = 6\) cm.

Triangular prism on horizontal rectangular base ABCD with AB = 10 cm and BC = 7 cm; T vertically above M, the midpoint of AD, with MT = 6 cm; line TB shown dashed

Diagram NOT accurately drawn

Calculate the size of the angle between \(TB\) and the base \(ABCD\).
Give your answer correct to 1 decimal place.

(4)

Mark scheme

Scheme	Marks
\(3.5^2 + 10^2\;(= 112.25)\) or \(6^2 + 3.5^2 + 10^2\;(= 148.25)\)	M1
\(\sqrt{\text{“}112.25\text{”}}\;(= 10.59..)\) or \(\sqrt{\text{“}148.25\text{”}}\;(= 12.17..)\)	M1
\(\tan(\text{“}x\text{”}) = 6 / \text{“}10.59..\text{”}\) or \(\sin(\text{“}x\text{”}) = 6 / \text{“}12.17..\text{”}\)	M1
29.5	A1
	(4)

Notes

M1: awrt 10.6 or 12.17

M1: (dep on M1M1)

A1: awrt 29.5