Higher January 2020 Paper 1R Q15
15 The diagram shows two right-angled triangles, \(DEF\) and \(EFG\).
Diagram NOT accurately drawn
Work out the length of \(EG\).
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
e.g. (\(EF\) =) 12cos40 (= 9.19…) or (\(FD\) =) 12sin40 (= 7.71…) and (\(EF\) =) \(\sqrt{12^2 - \text{“}7.71\text{”}^2}\) (= 9.19…) | M2 |
e.g. \(\dfrac{\text{“}9.19\text{”}}{EG} = \tan 28\) or \(\tan 62 = \dfrac{EG}{\text{“}9.19\text{”}}\) or \(\dfrac{\text{“}9.19\text{”}}{FG} = \sin 28\) (= 19.5…) and \(\text{“}19.5\text{”}^2 - \text{“}9.19\text{”}^2\) (= 298.9…) | M1 |
| 17.3 | A1 |
| (4) | |
| (4 marks) |
Notes
M2: complete method to find \(EF\)
(if not M2 then M1 for a correct statement involving \(EF\) e.g. \(\dfrac{EF}{12} = \cos 40\))
M1: (dep on M2) for a correct trig statement involving \(EG\) or complete method to find \(FG\) and a correct start to Pythagoras process
(corrected from the printed mark scheme: the printed “\(\tan 62 = \dfrac{EG}{\text{“}19.9\text{”}}\)” should have \(EF\) = “9.19” in the denominator)
A1: accept 17.2 – 17.3