Higher November 2024 Paper 1 Q12
12 \(ABC\) is a right-angled triangle.
\(D\) is a point on \(BC\)
Diagram NOT accurately drawn
\(AB = 4250\) m angle \(BAD = 47^\circ\) angle \(BCA = 24^\circ\)
Work out the length of \(DC\)
Give your answer correct to the nearest integer.
(4)
| Scheme | Marks |
|---|---|
eg \(\tan 47 = \dfrac{(BD)}{4250}\) or \(\tan 24 = \dfrac{4250}{(BC)}\) or \(\tan(47 + \text{“}19\text{”}) = \dfrac{(BC)}{4250}\) or \(\dfrac{(BD)}{\sin 47} = \dfrac{4250}{\sin 43}\) or \((AD =)\;\dfrac{4250}{\cos 47}\;(= 6231.686\ldots)\) or \((AD =)\;\dfrac{4250}{\sin 43}\;(= 6231.686\ldots)\) or \((AC =)\;\dfrac{4250}{\sin 24}\;(= 10\,449.021\ldots)\) or \((AC =)\;\dfrac{4250}{\cos 66}\;(= 10\,449.021\ldots)\) | M1 |
eg \((BD =)\;4250\tan 47\;(= 4557.567\ldots)\) or \((BC =)\;\dfrac{4250}{\tan 24}\;(= 9545.656\ldots)\) or \((BD =)\;\dfrac{4250}{\sin 43} \times \sin 47\;(= 4557.567\ldots)\) or \(\dfrac{(DC)}{\sin\text{“}19\text{”}} = \dfrac{\text{“}10449\ldots\ldots\text{”}}{\sin\text{“}137\text{”}}\) or \(\dfrac{(DC)}{\sin\text{“}19\text{”}} = \dfrac{\text{“}6231.686\text{”}}{\sin 24}\) or \((BC =)\;4250 \times \tan(47 + \text{“}19\text{”})\;(= 9545.656\ldots)\) or \((DC^2 =)\;\text{“}6231\text{”}^2 + \text{“}10449\text{”}^2 - 2 \times \text{“}6231\text{”} \times \text{“}10449\text{”} \times \cos 19\) | M1 |
eg “9545.656” – “4557.567” (= 4988.089) or \((DC =)\;\dfrac{\text{“}6231.686\text{”}}{\sin 24} \times \sin 19\) or \((DC =)\;\dfrac{\text{“}10449\ldots\ldots\text{”}}{\sin\text{“}137\text{”}} \times \sin\text{“}19\text{”}\) or \((DC =)\sqrt{\text{“}6231\text{”}^2 + \text{“}10449\text{”}^2 - 2 \times \text{“}6231\text{”} \times \text{“}10449\text{”} \times \cos 19}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 4988 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a complete method
A1: allow in the range 4932 – 4990