4MA0 Higher January 2017 Paper 4 Q21
21 The diagram shows a cuboid \(ABCDEFGH\).
Diagram NOT accurately drawn
\(AB = 21\) cm and \(CH = 9\) cm.
\(K\) is the point on \(EH\) such that angle \(AKB = 68^\circ\) and \(BK = 16.5\) cm.
(a) Calculate the size of angle \(BAK\).
Give your answer correct to 1 decimal place. (3)
Give your answer correct to 1 decimal place. (3)
(b) Calculate the size of the angle between the line \(BK\) and the plane \(ABCD\).
Give your answer correct to 1 decimal place. (2)
Give your answer correct to 1 decimal place. (2)
| Scheme | Marks |
|---|---|
| Eg \(\dfrac{16.5}{\sin BAK} = \dfrac{21}{\sin 68}\) or \(\dfrac{\sin BAK}{16.5} = \dfrac{\sin 68}{21}\) | M1 |
(\(\sin BAK =\)) \(\dfrac{16.5 \times \sin 68}{21}\) or 0.728(5016...) oe or (\(BAK =\)) \(\sin^{-1}\left(\dfrac{16.5 \times \sin 68}{21}\right)\) or (\(BAK =\)) \(\sin^{-1}\)(0.728(5016...)) oe | M1 |
| 46.8 | A1 |
| (3) |
Notes
M1: For a correct equation using the Sine Rule
A1: Accept 46.7(609...) rounded or truncated to at least 1dp
| Scheme | Marks |
|---|---|
| \(\sin\alpha = \dfrac{9}{16.5}\) or (\(\alpha =\)) \(\sin^{-1}\left(\dfrac{9}{16.5}\right)\) | M1 |
| 33.1 | A1 |
| (2) | |
| (5 marks) |
Notes
M1: Or for a correct equation using the Sine Rule
A1: Accept 33.0(557...) rounded or truncated to at least 1dp