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NSWMaths Standard 2Quick questions

Year 12: Measurement

Quick questions on The sine rule for HSC Maths Standard 2 (including the ambiguous case)

10short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the sine rule?
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For any triangle ABCABC with sides aa, bb, cc opposite angles AA, BB, CC:
What is when to use it?
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Use the sine rule when you have a matched pair (a side and its opposite angle) plus one other piece of information.
What is the ambiguous case (SSA)?
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When you know two sides and a non-included angle, the situation is sometimes ambiguous because there can be two different triangles with those measurements.
What is strategy in the exam?
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State the rule. Substitute. Compute. If you get sin⁡Y=k\sin Y = k, check whether 180°−sin⁡−1k180\degree - \sin^{-1} k also gives a valid triangle (sum of angles less than 180°180\degree with the known angle).
What is surveying (Australian context)?
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A surveyor stands at point AA and measures point BB at bearing 060°060\degree true and point CC at bearing 135°135\degree true. From BB, CC is at bearing 200°200\degree true, and the distance AB=250AB = 250 m.
What is ambiguous SSA?
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Triangle: A=30°A = 30\degree, a=4a = 4 cm, b=6b = 6 cm. Find BB.
What is forgetting the second solution in SSA?
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sin⁡Y=k\sin Y = k has two solutions: sin⁡−1k\sin^{-1} k and 180°−sin⁡−1k180\degree - \sin^{-1} k. Always check both before discarding.
What is wrong calculator mode?
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Use degrees (DEG), not radians (RAD), unless the question explicitly uses radians. Standard 2 uses degrees.
What is rounding too early?
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Carry the unrounded values through to the last step.
What is using the sine rule for SAS or SSS?
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Those need the cosine rule. :::

All Maths Standard 2Q&A pages