4MA0 Higher January 2013 Paper 4 Q25
25
Diagram NOT accurately drawn
The diagram shows a vertical flagpole in Chennai, India.
The point \(A\) is at the top of the flagpole.
The point \(B\) is at the foot of the flagpole.
There is a platform at the point \(D\) on the flagpole.
\(B\) and \(C\) are points on horizontal ground.
\(AD\) = 16.5 m
The angle of elevation of \(A\) from \(C\) is 69°
The angle of elevation of \(D\) from \(C\) is 59°
Calculate the height, \(AB\), of the flagpole.
Give your answer correct to 3 significant figures.
(6)
| Scheme | Marks |
|---|---|
| \(\angle ADC = 149°\) or \(\angle CAD = 21°\) | B1 |
\(\dfrac{AC}{\sin 149°} = \dfrac{16.5}{\sin 10°}\) or \(\dfrac{CD}{\sin 21°} = \dfrac{16.5}{\sin 10°}\) | M1 |
\((AC =)\ \dfrac{16.5 \sin 149°}{\sin 10°}\) or \((CD =)\ \dfrac{16.5 \sin 21°}{\sin 10°}\) | M1 |
| \((AC =)\) 48.938… or \((CD =)\) 34.052… | A1 |
| \((AB =)\) “48.938…” × sin 69° or 45.6(88…) or \((BD =)\) “34.052…” × sin 59° or 29.1(88…) | M1 |
| 45.7 | A1 |
| (6) |
Notes
B1: May be stated or marked on diagram
M1: for correct substitution in Sine Rule
M1: for correct rearrangement
A1: for correct length of \(AC\) or \(CD\) (rounded or truncated to at least 3 sf)
M1: rounded or truncated to at least 3 sf
A1: for ans which rounds to 45.7
Alternative scheme
| Scheme | Marks |
|---|---|
| \((BD =)\ BC \tan 59°\) oe | M1 |
| \(BD + 16.5 = BC \tan 69°\) oe | M1 |
| \(BD + 16.5 = \dfrac{\tan 69°}{\tan 59°}BD\) oe | M1 |
| \(\left(\dfrac{\tan 69°}{\tan 59°} - 1\right)BD = 16.5\) or \(0.5652\ldots BD = 16.5\) oe | M1 |
| \((BD =)\) 29.188… | A1 |
| Answer: 45.7 | A1 |
Notes
M1: Accept any clear notation throughout
M1: for equation in one variable
M1: for correct equation for one variable in the form \(ax = b\)
A1: for value which rounds to 29.2
A1: for ans which rounds to 45.7