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NSWMaths Standard 2Quick questions

Year 12: Measurement

Quick questions on The cosine rule for HSC Maths Standard 2

11short 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 cosine rule for sides (SAS)?
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For any triangle ABCABC with sides aa, bb, cc opposite angles AA, BB, CC:
What is the cosine rule for angles (SSS)?
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Rearrange to find an angle from three sides:
What is when to use it?
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For AAS or SSA, use the sine rule instead.
What is identifying the included angle?
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The included angle is the angle between the two given sides. In a worded problem, look for "the angle at BB between ABAB and BCBC" or "an angle of 60°60\degree between the two roads".
What is connection to Pythagoras?
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When C=90°C = 90\degree, cos⁡C=0\cos C = 0 and the cosine rule reduces to c2=a2+b2c^2 = a^2 + b^2, which is Pythagoras. The cosine rule is the generalisation of Pythagoras to non-right-angled triangles.
What is three sides, find an angle?
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A triangle has sides 55 cm, 77 cm and 1010 cm. Find the angle opposite the 77 cm side.
What is coastal navigation (Australian context)?
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A yacht sails from Sydney Heads on a bearing of 130°130\degree for 2525 km, then changes course to bearing 200°200\degree for 4040 km. How far from the starting point is the yacht?
What is forgetting to take the square root?
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c2c^2 is not cc. Take the positive root.
What is sign error with obtuse angles?
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cos⁡\cos of an angle between 90°90\degree and 180°180\degree is negative. The product −2abcos⁡C-2 a b \cos C becomes positive, so the formula effectively adds.
What is trying SAS or SSS with the sine rule?
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It cannot work because the sine rule needs a matched (angle, opposite side) pair, which SAS and SSS do not give.
What is rounding mid-computation?
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Carry intermediate values to at least four decimal places. The final answer can lose accuracy quickly otherwise. :::

All Maths Standard 2Q&A pages