The Cosine Rule (HSC SSCE Mathematics Standard): Flashcards

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The Cosine Rule
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Type of triangles cosine rule works for

Any triangle, not just right-angled triangles

What you need to find a side using cosine rule

Two sides and the included angle

What you need to find an angle using cosine rule

All three sides

Included angle definition

The angle between two sides

Formula to find side aa opposite angle AA

a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc \cos A

Formula for cos⁡A\cos A when all sides known

cos⁡A=b2+c2−a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}

Calculator mode for angles in degrees

Degree mode

Function to find angle from cosine value

Inverse cosine (cos⁡−1\cos^{-1} or arccos)

Memory aid for finding side using cosine rule

SAS (Side-Angle-Side)

Memory aid for finding angle using cosine rule

SSS (Side-Side-Side)

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