When a triangle gives two sides and the angle between them, the law of cosines finds the third side: c² = a² + b² − 2ab·cos C. These free printable worksheets state each triangle and ask for the side c, rounded to one decimal place.
If they get stuck
The answer key prints on a separate page.
It is the Pythagorean theorem with a correction term: when C is a right angle cos C is zero and the formula collapses to a² + b² = c², and for any other angle the −2ab·cos C accounts for the lean. That is the fact the sheet is built to make visible, one triangle at a time.
It is a calculator worksheet and prints for that reason: the answer is an irrational number rounded off. A length is asked to one decimal place, the answer key gives the rounded value, and the step-by-step walk substitutes the two sides and the included angle before taking the square root.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Law of cosines, step by step