Higher June 2023 Paper 5 Q13
13 The diagram shows a triangle, ABC, with perpendicular height BD.
Not to scale
BC = 12 cm, angle BCD = 30° and angle BAD = 45°.
(a) Work out the length of BD. [3]
(b) Work out the exact length of AB.
Give your answer in its simplest form. [3]
Give your answer in its simplest form. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6 | 3 | M1 for sin 30 = \(\frac{BD}{12}\) oe B1 for sin 30 = 0.5 oe soi | Accept e.g. sin 30 = \(\frac{\sqrt{1}}{2}\) Do not allow B1 if contradicted |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(6\sqrt{2}\) or \(\frac{12}{\sqrt{2}}\) cao | 3 | B2 for \(\sqrt{72}\) or better OR M1 for \(\frac{their(a)}{\sin 45}\) [= \(AB\)] oe or 2(their (a))\(^2\) oe or \(\frac{12 \times \sin 30}{\sin 45}\) [= \(AB\)] B1 for sin 45 = \(\frac{\sqrt{2}}{2}\) or \(\frac{1}{\sqrt{2}}\) oe soi | For M1, accept \(\frac{their(a)}{\cos 45}\) [= \(AB\)] oe For M1 , accept e.g. \(\frac{their(a) \times \sin 90}{\sin 45}\) [= \(AB\)] M1 implied by e.g. 72 For B1 accept cos 45 = \(\frac{\sqrt{2}}{2}\) or \(\frac{1}{\sqrt{2}}\) oe Do not allow B1 if contradicted |