Higher June 2019 Paper 1R Q7
7 The diagram shows isosceles triangle \(ABC\).
Diagram NOT accurately drawn
\(AB = AC = 7.5\) cm.
The height of the triangle is 6 cm.
Calculate the area of the triangle.
(4)
| Scheme | Marks |
|---|---|
| \(7.5^2 - 6^2\) (= 20.25) | M1 |
| \(\sqrt{7.5^2 - 6^2}\) (= 4.5) | M1 |
| “4.5” × 6 oe | M1 |
| 27 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: OR for a correct trig statement involving one of the angles e.g. \(\cos BAM = \dfrac{6}{7.5}\) or \(\sin ABC = \dfrac{6}{7.5}\) where \(M\) is the midpoint of \(BC\)
M1: OR for a method to find one of the angles in the triangle e.g. \(BAM = \cos^{-1}\left(\dfrac{6}{7.5}\right)\) (= 36.8…) or \(ABC = \sin^{-1}\left(\dfrac{6}{7.5}\right)\) (= 53.1…)
M1: for a complete method to find the area of triangle \(ABC\) e.g. \(2 \times \dfrac{1}{2} \times 7.5 \times 6 \times \sin(\text{``}{36.8}\text{''})\) oe or \(2 \times \dfrac{1}{2} \times 7.5 \times \sqrt{7.5^2 - 6^2} \times \sin(\text{``}{53.1}\text{''})\) oe
A1: cao