Shape and Space 10

2 marks · Easy

In triangle XYZ, sides XY = 9 cm, XZ = 7 cm, and YZ = 12 cm. Angle YXZ is opposite side YZ. Can you use the sine rule to find angle YXZ? Explain your answer.

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Yes, because two sides and the angle opposite one of those sides are known. The sine rule can be used to find the unknown angle.

Must show: Reason relating to two sides and an opposite angle

Also accept: Yes; we know two sides and the angle opposite one unknown side, so the sine rule applies.; Yes, we have enough information to set up the sine rule for angle YXZ.

Common mistakes: Saying cosine rule is required.; Incorrectly stating 'no'.

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Marking points

B1 · 1 mark · Identifies that the sine rule can be used (yes).

B2 · 1 mark · Provides a correct reason based on known sides and available opposite angle/side.

Worked solution

Yes, you can use the sine rule because you know the lengths of two sides and the side opposite the required angle, which fits the conditions for the sine rule.