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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

*a*2 = *b*2 + *c*2 – 2*bc* 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