Students will learn what the law of cosines is and why it's true. After that, students will learn how to use the law of cosines to solve triangles. That is, students will learn how to determine all the unknown angles and side lengths of a triangle using the law of cosines, given SSS or SAS. They'll learn how to solve both word problems and mathematical ones.

Concude by giving your students this challenge:

Find the length \(x{:}\)

Here's the solution. There are only two changes I would make to this solution. The first, is to split the base of the first triangle into \(25 - x\) and \(x,\) instead of \(m\) and \(n.\) This gets you the quadratic \(-x^2 + 25x - 144.\) Solving, you get \(x = 9, 16.\) I would then choose \(x = 9,\) because it more closely matches the diagram. The second change I would make, is to use mixed numbers throughout, instead of decimals.

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