Higher January 2022 Paper 2 Q14
14 A zip wire is shown as the dashed line \(AC\) in the diagram.
Diagram NOT accurately drawn
The zip wire is supported by two vertical posts \(AB\) and \(CD\) standing on horizontal ground.
\(CD = 2.6\) m \(BD = 12\) m
The zip wire makes an angle \(x\) with the horizontal, as shown in the diagram.
The design of the zip wire requires the angle \(x\) to be at least 5°
Work out the least possible height of the post \(AB\)
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
\(12 \times \tan 5\;(= 1.05)\) or \(\tan 5 = \dfrac{\text{``}{y}\text{''}}{12}\) or \(12\tan 5\) or \(\tan 85 = \dfrac{12}{\text{``}{y}\text{''}}\) or \(\dfrac{12}{\tan 85}\) \(\dfrac{y}{\sin 5} = \dfrac{12}{\sin 85}\) oe or \((y =)\;1.04986\ldots\) oe | M1 |
| \((AB =)\;2.6 + \text{``}{1.05}\text{''}\) oe | M1 |
| 3.65 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: oe correct expression using tan or the sine rule
or
\(\sqrt{\left(\dfrac{12}{\cos 5}\right)^2 - 12^2}\) (= 1.04986…)
A1: allow awrt 3.65