Higher January 2019 Paper 1R Q20
20 Here is a cube \(ABCDEFGH\).
Diagram NOT accurately drawn
\(M\) is the midpoint of the edge \(GH\).
Find the size of the angle between the line \(MA\) and the plane \(ABCD\).
Give your answer correct to 1 decimal place.
(4)
| Scheme | Marks |
|---|---|
| Let \(N\) be the midpoint of \(BC\) | B1 |
| Let sides of cube have length \(2a\) cm \(AN^2 = 4a^2 + a^2\) \((= 5a^2)\) or \(AM^2 = 4a^2 + a^2 + 4a^2\) \((= 9a^2)\) | M1 |
| eg \(\tan MAN = \dfrac{2a}{\sqrt{\text{``}{5a^2}\text{''}}}\) or \(\sin MAN = \dfrac{2a}{\sqrt{\text{``}{9a^2}\text{''}}}\) | M1 |
| 41.8 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for recognising that required angle is \(MAN\) (could be marked on a diagram)
M1: any \(a \gt 0\) (\(a\) could be a number or a letter)
M1: correct trig statement for angle \(MAN\), any \(a \gt 0\) (\(a\) could be a number or a letter)
A1: 41.8 - 41.82