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The Cosine Rule is used in triangles where one is

August 12, 2022

The Cosine Rule is used in triangles where one is trying to relate all three sides to one angle. If you need to find the length of a side, you need to know the other two sides and the opposite angle.

Formula

a2 = b2 + c2 – 2bc cos(A)

Side a is the one you are trying to find. Sides b and c are the other two sides, and angle A is the angle opposite side a

Example

Christiano Ronaldo is taking a shot at a standard 24 foot goal post. He is 32 feet away from one goal post and 45 feet from the other. Through what angle can a goal be made?

Explanation : cosine rule

We will aply cosine tule to this problem because we know the three lengths.

24ft ^2 = 32ft ^2 + 45ft ^2 – 2(32ft)(45ft) cos θ θ = cos−1 (24 ft ^2 – 32 ft^2 – 45ft^2) / -2(32ft)(45ft)

θ = 30.8312430

CR7 would have to shoot the ball around 31 degrees to score a goal.

Sources

Section 4: Sine and cosine rule. (n.d.). Retrieved August 11, 2022, from https://www.cimt.org.uk/projects/mepres/step-up/sect4/index.htm

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