Higher June 2024 Paper 2 Q12
12. The diagram below shows a vertical cliff which is 35 metres high.
Pierre is standing at point P.
From point P, the angle of elevation to the top of the cliff is 72°.
Diagram not drawn to scale
Pierre sees this warning sign.
Warning!
Coastal Erosion.
It is not safe to stand within
10 m of the base of the cliff.
Is Pierre standing a safe distance from the base of the cliff? [4]
Yes ☐ No ☐
Show how you decide.
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{35}{\tan(72)}\) or \(35\tan(90 - 72)\) or \(\dfrac{35\sin(90-72)}{\sin(72)}\) or \(\sqrt{\left(\dfrac{35}{\sin(72)}\right)^2 - 35^2}\) or \(\sqrt{(36.8..)^2 - 35^2}\) | M2 | Allow an alternative full method M1 for \(\tan(72) = \dfrac{35}{dist}\) or \(\tan(90-72) = \dfrac{dist}{35}\) or \(\dfrac{dist}{\sin(90-72)} = \dfrac{35}{\sin(72)}\) oe or \((36.8..)^2 - 35^2\) |
| 11.3(7…) or 11.4 (m) AND Yes, indicated or implied. | A2 | A1 for one of the following
|
| (4) |