Higher June 2022 Unit 2 Q15
15.
Diagram not drawn to scale
Calculate the size of \(X\hat{Y}Z\). [3]
\(X\hat{Y}Z =\) ……………°
From the formula list: In any triangle \(ABC\): Cosine rule \(a^2 = b^2 + c^2 - 2bc\cos A\)
| Scheme | Marks | Comments | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (cos XYZ =) \(\dfrac{34^2 + 55^2 - 73^2}{2 \times 34 \times 55}\) \(\left(= \dfrac{-287}{935}\right.\) OR –0·30695…) | M2 | Award M2 for use of cosine rule to find YXZ (= 45·8…°) or XZY (= 26·3…°) AND subsequent use of the sine rule to find the angle XYZ. Award M1 for 732 = 342 + 552 – 2×34×55×cos XYZ | |||||||||||||||
| (XYZ =) 107·8(75…°) or 107·9(°) or 108(°) | A1 | If no marks awarded, award SC1 for one of the following:
|