Intermediate November 2017 Unit 2 Q15
15. The diagram shows two right-angled triangles, joined together along a common side.
\(S\widehat{P}Q\) = 90°, \(S\widehat{Q}R\) = 90°, \(S\widehat{Q}P\) = 38°, PS = 8 cm and QR = 15 cm.
Diagram not drawn to scale
Calculate the size of angle \(x\). [6]
| Scheme | Marks | Comments |
|---|---|---|
| QS = \(\dfrac{8}{\sin 38}\) | M2 | M1 for \(\dfrac{8}{\text{QS}}\) = sin 38. Accept M1 for \(\dfrac{\text{QS}}{\sin 90} = \dfrac{8}{\sin 38}\) M2 for QS = \(\dfrac{8 \times \sin 90}{\sin 38}\) |
| = 13 or 12·99(..) | A1 | |
| tan x = \(\dfrac{15}{12.99(..)}\) | M1 | F.T. ‘their 12.99(..)’, stated or shown on diagram. |
| x = tan−1 (15/12·99…) | m1 | |
| = 49(·098..°) | A1 | Mark final answer. If FT leads to a non-integer value, allow to the nearest degree. |