Higher January 2020 Paper 1 Q9
9 Here is a right-angled triangle.
Diagram NOT accurately drawn
Calculate the length of \(PQ\).
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
\(\cos 63 = \dfrac{24.3}{(PQ)}\) or \(\sin 27 = \dfrac{24.3}{(PQ)}\) or \(\dfrac{(PQ)}{\sin 90} = \dfrac{24.3}{\sin 27}\) or \(\dfrac{\sin 90}{(PQ)} = \dfrac{\sin 27}{24.3}\) oe | M1 |
\((PQ =)\; \dfrac{24.3}{\cos 63}\) or \((PQ =)\; \dfrac{24.3}{\sin 27}\) or \((PQ) = \dfrac{24.3}{\sin 27} \times \sin 90\) | M1 |
| 53.5 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct trigonometric ratio
OR M2 (for both M1 marks) for
\((RQ =)\; 24.3 \times \tan 63\; (= 47.6914..)\) and
\((PQ =)\; \sqrt{\text{‘}47.6914\text{’}^2 + 24.3^2}\) oe
M1: for a correct rearrangement for \(PQ\)
A1: Accept 53.5 – 53.53