Higher June 2024 Paper 3 Q18
18 Here is triangle A.

Not drawn accurately
(a) Use the sine rule to show that \(\quad x = 64^\circ \quad\) to the nearest degree. [3 marks]
(b) Here is triangle B.

Not drawn accurately
Anna thinks that \(w\) must be \(64^\circ\) to the nearest degree.
She says,
“This is because triangle B has two sides and one angle the same as triangle A.”
Without further calculation, is she correct?Tick a box.
- Yes
- No
Give a reason for your answer. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{\sin x}{11} = \dfrac{\sin 35}{7}\) or \(\dfrac{11}{\sin x} = \dfrac{7}{\sin 35}\) | M1 | oe equation |
| \(\sin x = \dfrac{11 \sin 35}{7}\) or \(\sin x = 0.901\ldots\) or \(\sin^{-1} \dfrac{11 \sin 35}{7}\) or \(\sin^{-1} 0.901\ldots\) | M1dep | oe equation with \(\sin x\) as the subject |
| [64.2, 64.4] with correct working seen | A1 |
Additional guidance
| 0.901… may be seen as 0.9 for M marks | |
| Only using \(x = 64\) in sine rule | M0 |
| [64.2, 64.4] with no appropriate working | M0M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| No and correct reason indicating that \(35^\circ\) is a different angle or No and correct reason indicating that 7 cm is a different side | B1 | oe eg correct reasons 35 is between 7 and 11 this time 35 is not opposite 7 A is SSA but B is SAS |
Additional guidance
| Ignore irrelevant reasons with a correct reason | |
| ‘Yes’ ticked | B0 |
| ‘No’ ticked and states: | |
| (A and B are) not congruent | B1 |
| This triangle is SAS but the other one is not | B1 |
| The sides are not opposite the same angles | B1 |
| 35 is in a different position compared to the sides | B1 |
| 35 is in a different position | B0 |
| 7 is in a different position compared to the angles | B1 |
| 7 is in a different position | B0 |
| 7 was opposite 35 and is now adjacent | B1 |
| 7 was opposite and is now adjacent | B0 |
| Sides and angles are in different places | B0 |
| Sides are in different places | B0 |
| There is no value opposite the 35 | B0 |
| The angle is in a different position compared to the sides | B0 |
| It is a different size | B0 |
| It is a different shape | B0 |
| \(w\) is 72(.3…) or use of sine rule (question says ‘without further calculation’) | B0 |