Higher June 2019 Unit 2 Q14
14. The diagram shows a triangle \(ABC\) and a circle with centre \(A\).
The points \(B\) and \(D\) lie on the circumference of the circle.
The radius of the circle is 8 cm.
The length of the line \(AC\) is 19 cm.
The area of triangle \(ABC\) is 70 cm2.
Diagram not drawn to scale
Calculate the area of the sector \(ABD\). [5]
| Scheme | Marks | Comments |
|---|---|---|
| sin BAD = (2×70)/(8×19) or equivalent | M2 | Allow any unambiguous indication of angle BAD. M1 for the correct use of the formula when sinBAD is not the subject, for example: 70 = 1/2×8×19×sinBAD. |
| (BAD=) 67(.08…°) | A1 | Allow any answer that rounds to 67(°). |
| (Area of sector ABD=) 67(.08…)/360×π×82 | M1 | Accept 292.9(…)/360×π×82 OR 293/360×π×82 for the area of the major sector ABD. FT their derived or stated value of angle BAD. |
| Accept answers in the range 37.4(cm2) to 37.5(cm2) OR 37(cm2) | A1 | Accept an answer in the range 163.5(cm2) to 163.7(cm2) OR 164(cm2) for the area of the major sector ABD. |