Higher June 2017 Paper 4 Q14
14 The diagram shows triangle ABC with D on AC and E on AB.
DE is a straight line.
Not to scale
AD = 28 m, AE = 41 m, DE = 22 m and BC = 64 m.
Calculate the length CD. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 92 or 92.28 to 92.6 | 6 | M3 for correct explicit cos rule to find angle A in ADE with cos as subject. [cos A =] \(\dfrac{28^2 + 41^2 - 22^2}{2 \times 28 \times 41}\) oe soi | accept any correct method implied by [A=] 30.3 to 30.4 |
| or | |||
| M2 for correct implicit form of the cos rule to find angle A \(22^2 = 28^2 + 41^2 - 2 \times 28 \times 41 \times \cos A\) | |||
| or | |||
| M1 for either of the above forms with only one error | |||
| AND | |||
| M2 for correct sine rule e.g. \(\dfrac{64 \times \sin 72}{\sin \mathit{their}A}\) oe soi or M1 for \(\dfrac{64}{\sin \mathit{their}A} = \dfrac{[\ldots]}{\sin 72}\) oe | |||
| if 0 scored SC1 for explicit form of cos rule to find angle D or E in ADE e.g. [cos D =] \(\dfrac{28^2 + 22^2 - 41^2}{2 \times 28 \times 22}\) | |||