Intermediate June 2017 Unit 2 Q21
21. The area of triangle ABD, shown in the diagram below, is 35 cm2.
AD = 5 cm and BC = 32 cm.
D is on the line AC, and BD is perpendicular to AC.
Diagram not drawn to scale
Calculate the size of angle \(x\).
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{\text{BD} \times 5}{2}\) = 35 | M1 | |
| BD = 14(cm) | A1 | May be seen on the diagram. Note : If they state that AB = 14cm, or indicate on the diagram that AB = 14cm then it is M0A0 as an incorrect method used for area of a right-angled triangle (however an unattached 14cm has to be given the benefit of the doubt and be awarded M1A1). |
| Cos x = \(\dfrac{14}{32}\) | M1 | FT ‘their stated or shown length BD’. FT has to use ‘their BD’ (not CD). |
| x = cos−1 0·4375 | m1 | |
| x = 64(°) | A1 | Accept answer rounded or truncated. [e.g. if their BD = 7, then accept 77(·36…°)] |