4MA0 Higher January 2016 Paper 3 Q20
20
Diagram NOT accurately drawn
Work out the area of triangle \(ABC\).
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{\sin A}{36} = \dfrac{\sin 48}{57}\) | M1 |
\(A = \sin^{-1}\left(\dfrac{\sin 48}{57} \times 36\right)\) or \(A\) in range 27.9 − 28 | M1 |
| \(\dfrac{1}{2} \times 57 \times 36 \times \sin(180 - 48 - \text{"28"})\) (=995.49...) | M1 |
| 995 | A1 |
| (4) |
Notes
M1: or \(\dfrac{36}{\sin A} = \dfrac{57}{\sin 48}\)
M1: dep
M1: dep on the first M1
or \(\dfrac{1}{2} \times AC \times 36 \times \sin(48)\) with \(AC\) in range 74 – 74.5 or \(AC\) from a correct method
A1: for answer in the range 995 - 996
Alternative
| Scheme | Marks |
|---|---|
| Let \(BD\) be altitude of triangle \(BD = 36 \times \sin 48^\circ\) (= 26.7..) AND \(DC = 36 \times \cos 48^\circ\) (= 24.0..) | M1 |
| \(AD = \sqrt{57^2 - \text{"26.7.."}^2} = 50.331\) | M1 |
| \(\dfrac{1}{2} \times \text{“26.7..”} \times (\text{“24.0…”} + \text{“50.3…”})\) | M1 |
| 995 | A1 |
Notes
M1: correct method to find \(BD\) and \(DC\)
M1: dep
M1: dep on the first M1
A1: for answer in the range 995 - 996