Area of a Triangle (HSC SSCE Mathematics Standard): Flashcards

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Area of a Triangle
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Info needed for triangle area (non-right)

Two sides and the included angle

Included angle

The angle between the two sides being used

Area formula with sides bb, cc and angle AA

A=12bcsin⁡AA = \frac{1}{2}bc \sin A

SAS in triangle area context

Side-Angle-Side (two sides + included angle)

Calculator mode for sine values

Degree mode

Sine ratio in right triangle (derivation)

sin⁡C=ha\sin C = \frac{h}{a}

Height hh in terms of side aa and angle CC

h=asin⁡Ch = a \sin C

Requirement for angle in area formula

Must be the included angle (between the two sides)

Triangle vertex and side labelling

Vertices: AA, BB, CC; opposite sides: aa, bb, cc

Area principle (words)

Half × two sides × sine of included angle

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