Higher June 2022 Paper 3 Q12
12 \(ABC\) and \(ACD\) are right-angled triangles.
\(DC = 8\) cm
Angle \(ADC = 45^\circ\)
Angle \(ABC = 20^\circ\)
Work out the length of \(AB\).
Give your answer correct to 3 significant figures. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 23.4 | M1 | for stating that \(AC = 8\) or for a relationship that may be used to find \(AC\) eg (\(AC =\)) \(8 \times \tan 45\) or \(\tan 45 = \dfrac{AC}{8}\) |
| M1 | for relationship that may be used to find \(AB\), eg \(\sin(20) = \text{``}8\text{''} \div AB\) or (\(AB =\)) \(\dfrac{\text{``}8\text{''}}{\sin 20}\) | |
| A1 | for answer in the range 23.3 to 23.4 | |
| Alternative | ||
| M1 | for a relationship that may be used to find \(AD\) eg \(\cos(45) = 8 \div AD\) oe or (\(AD =\)) 11.3(13...) | |
| M1 | for a relationship that may be used to find \(AB\), eg \(\dfrac{AB}{\sin 45} = \dfrac{\text{``}11.3\text{''}}{\sin 20}\) | |
| A1 | for answer in the range 23.3 to 23.4 |
Additional guidance
May be seen on diagram
May use the sine rule
If an answer is given in the range in working and then rounded incorrectly award full marks.