4MA0 Higher June 2011 Paper 3 Q18
18
Diagram NOT accurately drawn
Triangle \(ABC\) is right-angled at \(B\).
Angle \(BAC = 32^\circ\)
\(AC\) = 47 m.
\(D\) is the point on \(AB\) such that angle \(BDC = 51^\circ\)
Calculate the length of \(BD\).
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| (\(BC\) =) 47 sin 32° | M1 |
| 24.906… at least 3 sf (may be implied by correct \(BD\)) | A1 |
| \(\tan 51^\circ = \dfrac{\text{“}24.906...\text{”}}{BD}\) or \(\tan 39^\circ = \dfrac{BD}{\text{“}24.906...\text{”}}\) | M1 |
| (\(BD\) =) \(\dfrac{\text{“}24.906...\text{”}}{\tan 51^\circ}\) or “24.906…” tan 39° | M1 |
| 20.2 | A1 |
| (Total 5 marks) |
Notes
M1: or for (\(CD\) =) \(\dfrac{47 \sin 32^\circ}{\sin 129^\circ}\)
A1: or for \(CD\) = 32.048… at least 2 sf (may be implied by correct \(BD\))
M1: or for \(\cos 51^\circ = \dfrac{BD}{\text{“}32.048...\text{”}}\)
M1: or for (\(BD\) =) “32.048…” cos 51°
A1: for answer rounding to 20.2 (20.1686…)