1MA0 Higher June 2016 Paper 2 Q17
17
Diagram NOT accurately drawn
\(ABC\) is a right-angled triangle.
\(D\) is a point on \(AB\).
Angle \(ACD = 30^\circ\)
\(AD = 10.4\) cm
\(DB = 5.2\) cm
\(AC = 18\) cm
Work out the size of the angle marked \(x\).
Give your answer correct to 1 decimal place. (4)
| Answer | Mark | Notes |
|---|---|---|
| 30.1 | 4 | M1 for a correct trigonometric statement to find an unknown angle, eg. \(\sin(30 + x)\) or \(\cos A = \dfrac{10.4 + 5.2}{18}\) or \(\dfrac{\sin ADC}{18} = \dfrac{\sin 30}{10.4}\) M1 for a complete method to find the angle, eg. \(\sin^{-1}\left(\dfrac{10.4 + 5.2}{18}\right)\) (= 60.07...) or \(\cos^{-1}\left(\dfrac{10.4 + 5.2}{18}\right)\) (= 29.92..) or \(\sin^{-1}\left(\dfrac{18 \times \sin 30}{10.4}\right)\) (= 59.92.. or 180 – 59.92.. = 120.07..) M1 (dep on M2) for a fully complete method to find angle \(x\), eg. "60.07..". – 30 or 60 – "29.92.." or 90 – "59.92.." A1 for answer in the range 30.07 to 30.1 OR M1 for \((BC^2 =)\ 18^2 - (10.4 + 5.2)^2\) or \(BC^2 + (10.4 + 5.2)^2 = 18^2\) M1 for \((BC =)\ \sqrt{18^2 - (10.4 + 5.2)^2}\) (= 8.97...) M1 (dep on M2) for a fully complete method to find angle \(x\), eg. \(\tan^{-1}\left(\dfrac{5.2}{\text{``}8.97...\text{''}}\right)\) A1 for answer in the range 30.07 to 30.1 |