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Trigonometry practice

Law of Cosines worksheets

Find a missing side from SAS data or a missing angle from SSS data, with acute and obtuse examples.

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Use the law of cosines. Substitute the labeled values, keep full precision, and round only the final answer.

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Read opposite pairs before choosing a law

Every diagram uses the standard pairs A and a, B and b, C and c. Law-of-sines sheets include the ambiguous SSA case and require every supplementary candidate to be checked. Law-of-cosines sheets mix side and angle tasks, including obtuse triangles.

Learning objective

What this activity builds

Select the correct law-of-cosines form, preserve calculator precision, and solve bounded SAS and SSS triangles.

Worked example

Given b = 7, c = 11, and A = 103°, find a.

a² = 7² + 11² - 2(7)(11)cos(103°), then take the positive square root.

Angle A is included between sides b and c, and side a is opposite A.

Teaching notes

Make the practice count

  • Match each side with its opposite angle before substituting.
  • Use degree mode for inverse cosine.
  • An obtuse angle must be opposite the longest side.

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Math SheetNameScoreTeacherDateLaw of CosinesUse the law of cosines to find the requested side or angle. Keep full calculator precision until the final answer, then round as directed.1.Given b = 9, c = 13, and included angle A = 52°, find side a. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.2.Given a = 10, b = 13, and c = 16, find angle C. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.Angles are in degrees. Round only final answers.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateLaw of CosinesUse the law of cosines to find the requested side or angle. Keep full calculator precision until the final answer, then round as directed.3.Given a = 9, b = 14, and c = 18, find angle C. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.4.Given b = 15, c = 17, and included angle A = 73°, find side a. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.Angles are in degrees. Round only final answers.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateLaw of CosinesUse the law of cosines to find the requested side or angle. Keep full calculator precision until the final answer, then round as directed.5.Given b = 9, c = 12, and included angle A = 132°, find side a. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.6.Given a = 9, b = 10, and c = 12, find angle C. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.Angles are in degrees. Round only final answers.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateLaw of CosinesUse the law of cosines to find the requested side or angle. Keep full calculator precision until the final answer, then round as directed.7.Given b = 9, c = 14, and included angle A = 156°, find side a. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.8.Given a = 12, b = 15, and c = 20, find angle C. Round the final answer to the nearest tenth.ABCcabReference sketch; calculate using the givens.Angles are in degrees. Round only final answers.math-sheet.comPage 4 of 4

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Solve AAS, ASA, and ambiguous SSA triangles, including cases with zero, one, or two valid solutions.

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