4400 Higher June 2010 Paper 3 Q20
20
Diagram NOT accurately drawn
\(A\), \(B\) and \(C\) are points on horizontal ground.
\(C\) is due West of \(B\).
\(A\) is due South of \(B\) and \(AB = 40\) m.
There is a vertical flagpole at \(B\).
From \(A\), the angle of elevation of the top of the flagpole is 13°.
From \(C\), the angle of elevation of the top of the flagpole is 19°.
Calculate the distance \(AC\).
Give your answer correct to 3 significant figures.
(6)
| Scheme | Marks |
|---|---|
| 13° or 19° angle of elevation identified | B1 |
| M1 | |
| \(\tan 19^\circ = \dfrac{\text{“}9.2347...\text{”}}{BC}\) | M1 |
\((BC =)\ \dfrac{\text{“}9.2347...\text{”}}{\tan 19^\circ}\) or \(\dfrac{40 \tan 13^\circ}{\tan 19^\circ}\) or 26.819... | M1 |
| \(40^2 + \text{“}26.819...\text{”}^2\) | M1 |
| 48.2 | A1 |
| (6) | |
| (6 marks) |
Notes
B1: On diagram or implied by working
M1: for 40 tan 13° or 9.2347... rounded or truncated to at least 2 sf or any complete, correct method of finding the height of the flagpole
M1: or for \(\tan 71^\circ = \dfrac{BC}{\text{“}9.2347...\text{”}}\)
M1: dep on first two M1s
for \(40^2 + \text{“}26.819...\text{”}^2\) or for complete, correct method of finding length of \(AC\)
A1: for ans rounding to 48.2 (48.1590...)
Award 6 marks for an answer which rounds to 48.2, if it has been obtained by a mathematically correct method