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Printable Law of Cosines Worksheet | Grade 10–12 Math
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This Law of Cosines worksheet helps students solve complete triangles from SAS and SSS information, then extend to area with ½ab·sin C. Students find missing sides and angles, keep full calculator precision, round only at the end, and check that their results make geometric sense.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Law of Cosines and Law of Sines to find missing triangle measurements- Skill Focus: Solving SAS and SSS triangles, plus area
- Format: 3 pages · 42 problems · Answer key included · PDF
- Best For: Trigonometry unit practice and review
- Time: 30–40 minutes
What's Inside
The worksheet has 3 pages and three parts. Part A has six SAS triangles, Part B has six SSS triangles, and Part C has three area problems. Each part opens with a worked example, and students sketch each triangle as they work. A 3-page answer key lists every side, angle, and area.
Skill Progression
- Guided practice: three worked examples model the SAS, SSS, and area methods step by step.
- Supported practice: Part A, six SAS triangles, where students find the third side and then both remaining angles using the worked example as a reference.
- Independent practice: Part B (six SSS triangles) and Part C (three area problems) with brief directions only.
The sequence follows gradual release: I Do, We Do, You Do.
Standards Alignment
HSG-SRT.D.11 — Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- After direct instruction: assign Parts A and B as in-class practice once students have seen the Law of Cosines derived.
- Before a quiz: use Part C as a short review of area with ½ab·sin C.
Formative tip: watch for students who round the third side early, since this shifts later angle values. Expect 30–40 minutes to complete.
Who It's For
Students in Grades 10–12 in Geometry, Algebra II, or Precalculus who already know the Law of Sines. Students who need extra support can work the worked examples first. Pair it with a Law of Cosines anchor chart or a direct instruction lesson.
This Grade 10–12 Law of Cosines worksheet targets HSG-SRT.D.11, where students use the Law of Cosines and Law of Sines to find unknown measurements in non-right triangles. Across 3 pages and 42 tasks, learners solve six SAS triangles, six SSS triangles, and three area problems using Area = ½ab·sin C, with a worked example opening each part. A 3-page answer key supports quick checking. Fisher & Frey (2014) describe gradual release of responsibility, moving from modeled examples to guided work to independent practice, as a reliable structure for building procedural fluency, and this worksheet follows that sequence. Students practice keeping full calculator precision, rounding to the nearest tenth at the end, and verifying that angle measures sum to 180°. It suits trigonometry units, review days, and assessment preparation for high school geometry and precalculus classes.
