4400 Higher June 2006 Paper 4 Q9
9
(a) A farmer arranges 90 m of fencing in the form of an isosceles triangle, with two sides of length 35 m and one side of length 20 m.
Diagram NOT accurately drawn
Calculate the area enclosed by the fencing.
Give your answer correct to 3 significant figures.
(4)
(b) Later, the farmer moves the fencing so that it forms a different triangle, \(ABC\).
Diagram NOT accurately drawn
\(AB = 20\) m \(\qquad BC = 40\) m \(\qquad CA = 30\) m
Calculate the size of angle \(BAC\).
Give your answer correct to 1 decimal place.
(3)
| Scheme | Marks |
|---|---|
| \(35^2 - 10^2\) | M1 |
| 33 to 34 | A1 |
| \(\frac{1}{2} \times 20 \times\) “ht” | M1 |
| 335 | A1 |
| (4) |
Alternatives
\(20^2 = 35^2 + 35^2 - 2 \times 35 \times 35\cos A\) or \(\sin x = 10/35\) M1; 33(.2) A1; \(\frac{1}{2} \times 35^2 \times \sin\)“33.2” M1
\(35^2 = 35^2 + 20^2 - 2 \times 35 \times 20\cos B\) or \(\cos B = 10/35\) M1; 73(.4) A1; \(\frac{1}{2} \times 35 \times 20 \times \sin\)“73.4” M1
| Scheme | Marks |
|---|---|
| \(40^2 = 20^2 + 30^2 - 2 \times 20 \times 30\cos x\) | M1 |
| \(\cos x = \dfrac{20^2 + 30^2 - 40^2}{2 \times 20 \times 30}\) (= −0.25) | M1 |
| 104 to 105 | A1 |
| (3) | |
| (7 marks) |
Notes
M1: May be implied
or \(\cos x = \dfrac{-300}{1200}\) oe
A1: Scale drawing: M0A0