Higher January 2021 Paper 2R Q13
13 The diagram shows two hot air balloons.
\(A\) is a point on the base of one of the balloons and \(B\) is a point on the base of the other balloon.
Diagram NOT accurately drawn
The distance between \(A\) and \(B\) is 500 metres.
The angle of depression of \(B\) from \(A\) is 23°
Calculate the vertical height of \(A\) above \(B\).
Give your answer correct to one decimal place.
(3)
| Scheme | Marks |
|---|---|
\(\sin 23° = \dfrac{\text{“}h\text{”}}{500}\) oe or \(\cos 67° = \dfrac{\text{“}h\text{”}}{500}\) oe or \(\dfrac{\text{“}h\text{”}}{\sin 23°} = \dfrac{500}{\sin 90°}\) or \(\dfrac{\sin 23}{\text{“}h\text{”}} = \dfrac{\sin 90}{500}\) oe or \(\cos 23° = \dfrac{\text{“}x\text{”}}{500}\) oe or “\(x\)” = 500 cos 23° (= 460.25..) and “\(h\)”\(^2 = 500^2 - (\text{“}460.25\ldots\text{”})^2\) oe | M1 |
“\(h\)” = 500 × sin 23° oe or “\(h\)” \(= \sqrt{500^2 - (\text{“}460.25\ldots\text{”})^2}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 195.4 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct expression involving “h”
A1: 195 – 195.4