Higher November 2019 Paper 3 Q26
26 Here is a triangular sail.
Not drawn accurately
(a) Vicky needs to buy waterproofing liquid for the sail.
She will put 3 coats of liquid on each side of the sail.
A litre of liquid covers 8.5 square metres of sail.
How many 1-litre bottles of liquid does Vicky need? [3 marks]
(b) Another sail is joined to the first sail as shown.
Not drawn accurately
\(x\) is an acute angle.
Work out the size of angle \(x\). [5 marks]
Answer in degrees
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{2} \times 9.7 \times 3.8 \times \sin 73^\circ\) or 17.6… | M1 | oe |
| their \(17.6\ldots \times 6 \div 8.5\) or \(105.7\ldots \div 8.5\) or 12.4… | M1dep | oe |
| 13 | A1 |
Additional guidance
| \(\dfrac{1}{2} \times 9.7 \times 3.8 = 18.43 \quad 18.43 \times 6 \div 8.5 = 13.0\ldots\) | M0M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| \(9.7^2 + 3.8^2 - 2 \times 9.7 \times 3.8 \times \cos 73^\circ\) or \(94.09 + 14.44 - 73.72\cos 73^\circ\) or 86.976… or 86.98 or 87 | M1 | oe |
| \(\sqrt{\text{their } 86.976\ldots}\) | M1dep | |
| 9.3(2…) or 9.33 | A1 | |
| \(\dfrac{\sin x}{\text{their } 9.32\ldots} = \dfrac{\sin 42}{8}\) or \(\sin^{-1}[0.7778,\ 0.7804]\) | M1 | oe their 9.32… must be their length of the vertical line |
| [51, 51.3] | A1ft | ft their 9.3(2…) or 9.33 |
Additional guidance
Their 9.32… must come from M1M1 or be clearly identified in working or on the diagram as the length of the vertical line