Geometry II (AQA GCSE Further Maths): Flashcards

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The cosine rule
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What does the cosine rule help find?

Unknown sides or angles in any triangle

Two scenarios when cosine rule is useful

Two sides + included angle OR all three sides known

Cosine rule formula to find side aa

a2=b2+c22bccosAa^2 = b^2 + c^2 - 2bc \cos A

Cosine rule formula to find angle AA

cosA=b2+c2a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}

What does SAS mean for cosine rule?

Side-Angle-Side; use to find a side length

What does SSS mean for cosine rule?

Side-Side-Side; use to find an angle

Standard triangle notation: lowercase vs uppercase letters

Lowercase = side lengths; Uppercase = opposite angles

Alternative cosine rule formula for side bb

b2=a2+c22accosBb^2 = a^2 + c^2 - 2ac \cos B

Conceptual way to think of cosine rule

Pythagoras with an extra correction term

Common mistake when finding side length with cosine rule

Forgetting to square root the result

What does negative cosine value indicate for an angle?

An obtuse angle (greater than 90°)

Types of triangles cosine rule works for

Any triangle: acute, obtuse, or right-angled

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