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Trigonometry practice

Law of Sines worksheets

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

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Solve in degrees. Show the sine proportion, check every SSA candidate, and round only final answers.

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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

Use the law of sines to solve valid triangles and classify every bounded SSA case without accepting a degenerate angle set.

Worked example

Given A = 30°, a = 7, and b = 10, how many triangles are possible?

Two triangles.

sin(B) = 10 sin(30°) / 7. Both the inverse-sine angle and its supplement leave a positive third angle, so both solutions are valid.

Teaching notes

Make the practice count

  • Pair each angle with its opposite lowercase side.
  • For SSA, always test the supplementary inverse-sine candidate.
  • Reject a candidate when the third angle is zero or negative.

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Choose AAS, ASA, or specific SSA outcomes. Selected cases are balanced across the sheet; keep the seed to reproduce it.

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Math SheetNameScoreTeacherDateLaw of SinesSolve each triangle in degrees. Show the sine proportion, reject any angle set that does not total 180°, and round only final answers to the selected precision.1.Given A = 25°, a = 8, and b = 10, determine whether zero, one, or two triangles are possible. Solve every valid triangle to the nearesttenth.ABCcabLabel schematic only; does not assert existence2.Given A = 53°, B = 42°, and a = 13, solve triangle ABC. Round final values 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 SinesSolve each triangle in degrees. Show the sine proportion, reject any angle set that does not total 180°, and round only final answers to the selected precision.3.Given A = 30°, a = 4, and b = 12, determine whether zero, one, or two triangles are possible. Solve every valid triangle to the nearesttenth.ABCcabLabel schematic only; does not assert existence4.Given A = 26°, B = 88°, and c = 7, solve triangle ABC. Round final values 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 SinesSolve each triangle in degrees. Show the sine proportion, reject any angle set that does not total 180°, and round only final answers to the selected precision.5.Given A = 65°, a = 18, and b = 14, determine whether zero, one, or two triangles are possible. Solve every valid triangle to the nearesttenth.ABCcabLabel schematic only; does not assert existence6.Given A = 31°, a = 10.4, and b = 13, determine whether zero, one, or two triangles are possible. Solve every valid triangle to thenearest tenth.ABCcabLabel schematic only; does not assert existenceAngles are in degrees. Round only final answers.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateLaw of SinesSolve each triangle in degrees. Show the sine proportion, reject any angle set that does not total 180°, and round only final answers to the selected precision.7.Given A = 75°, a = 11, and b = 18, determine whether zero, one, or two triangles are possible. Solve every valid triangle to the nearesttenth.ABCcabLabel schematic only; does not assert existence8.Given A = 44°, B = 63°, and a = 11, solve triangle ABC. Round final values 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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Printable law of cosines worksheets preview

Trigonometry

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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