The Sine Rule (VCE SSCE General Mathematics): Flashcards

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The Sine Rule
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Purpose of the sine rule

Find missing sides/angles in non-right-angled triangles

When to use the sine rule

Two sides + opposite angle OR two angles + one side

Standard notation for triangle angles

Uppercase letters: AA, BB, CC

Relationship between sides and angles in notation

Side opposite its matching angle (e.g., aa opposite AA)

The sine rule formula

asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Flipped form of sine rule

sinAa=sinBb=sinCc\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

The ambiguous case definition

Two different triangles from same given information

When ambiguous case occurs

Two sides and angle NOT between them given

Side opposite the largest angle

The longest side

Angle sum in any triangle

A+B+C=180°A + B + C = 180°

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