Higher June 2023 Paper 2 Q8
8.
Diagram not drawn to scale
An aircraft is making its final approach ready to land.
The aircraft is:
- flying at 3° to the horizontal,
- 2·5 km horizontally from the start of the runway,
as shown on the diagram above.
Calculate the vertical height of the aircraft above the horizontal ground.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Degree symbol may be omitted throughout; lengths may be in metres throughout | ||
| Use of right-angled triangle with trigonometry with 3° or 87° correctly indicated with 2.5 used as a side. | S1 | Angle may be marked on diagram; trig ratio used may not be correct at this stage |
| (vertical height =) \(2.5\tan 3^\circ\) or \(\dfrac{2.5}{\tan 87^\circ}\) | M2 | M1 for \(\tan 3^\circ = \dfrac{?}{2.5}\) or \(\tan 87^\circ = \dfrac{2.5}{?}\) |
| 0.1(3...) (km) | A1 | Not from wrong working e.g. 2.5sin(3) If units are stated, they must be correct but ISW any attempt at a unit change after a correct answer has been seen Unsupported 0.1(3…) is awarded S1 only |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Use of right-angled triangle with trigonometry with 3° or 87° correctly indicated with 2.5 used as a side. | S1 | Angle may be marked on diagram; trig ratio used may not be correct at this stage |
| (vertical height =) \(\dfrac{2.5 \times \sin 3}{\sin 87}\) | M2 | M1 for \(\dfrac{2.5}{\sin 87} = \dfrac{x}{\sin 3}\) oe |
| 0.1(3...) (km) | A1 | Unsupported 0.1(3…) is awarded S1 only |
| (4) |