4MA0 Higher June 2016 Paper 3 Q16
16 \(ABCDEFGH\) is a cuboid.
Diagram NOT accurately drawn
The cuboid has
length 17 cm
width 5 cm
height 8 cm
Work out the size of the angle that \(AH\) makes with the plane \(EFGH\).
Give your answer correct to 1 decimal place.
(4)
| Scheme | Marks |
|---|---|
| angle \(AHF\) identified | M1 |
| (\(FH\)=) \(\sqrt{17^2 + 5^2}\) or \(\sqrt{314}\) (=17.7...) | M1 |
| \(\tan AHF = \dfrac{8}{\text{"17.7..."}}\) | M1 |
| 24.3 | A1 |
| (4) |
Notes
M1: may be implied by a correct calculation
M1: or (\(AH\) = ) \(\sqrt{17^2 + 5^2 + 8^2}\) (=19.4..) or \(\sqrt{378}\) or \(3\sqrt{42}\)
M1: dep on previous M1
or \(\cos AHF = \dfrac{\text{"17.7..."}}{\text{"19.4..."}}\) or
\(\sin AHF = \dfrac{8}{\text{"19.4..."}}\) ( × sin90) or
\(\cos AHF = \dfrac{\text{"19.4.."}^2 + \text{"17.7.."}^2 - 8^2}{2 \times \text{"19.4.."} \times \text{"17.7.."}}\)
A1: answer in range 24.2 − 24.4