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.
Kid stuck on one? You don’t just get the sheet.
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 this sheet, worked through a step at a time.
Find c by the law of cosines
