4MA0 Higher June 2017 Paper 4R Q22
22 \(ABCDEFGH\) is a cuboid.
Diagram NOT accurately drawn
\(AB = 16\) cm and \(HG = 15\) cm.
\(M\) is the midpoint of \(EH\).
\(BM\) makes an angle of 24° with the base \(EFGH\).
Calculate the height, \(BG\), of the cuboid.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| B1 | |
| \(\sqrt{8^2 + 15^2}\) or \(\sqrt{289}\) or 17 | M1 |
Eg \(\tan 24 = \dfrac{BG}{\sqrt{8^2 + 15^2}}\) or \(\tan 24 = \dfrac{BG}{17}\) or \(\dfrac{BG}{\sin 24} = \dfrac{\sqrt{8^2 + 15^2}}{\sin(90 - 24)}\) or \(\dfrac{BG}{\sin 24} = \dfrac{17}{\sin 66}\) (\(BG =\)) 17tan24 or (\(BG =\)) \(\dfrac{17}{\sin 66} \times \sin 24\) | M1 |
| 7.57 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: Identifying correct triangle
M1: Complete method to find \(MG\)
M1: Dep
For a correct equation involving \(BG\) or a correct expression for \(BG\)
Implies B1
A1: Accept 7.56 – 7.57