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Printable Law of Cosines Notes Worksheet | Grades 10-12 Math
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This guided-notes worksheet helps students decide when the Law of Cosines applies and use it to find a missing side or angle. Students complete 30 fill-in items across 2 pages, connect the formula to the Pythagorean Theorem, and finish with four independent problems.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Law of Cosines to find missing sides and angles in triangles.- Skill Focus: Choosing and applying the Law of Cosines (SAS, SSS)
- Format: 2 pages · 30 problems · Answer key included · PDF
- Best For: First lesson on oblique triangles
- Time: 25–35 minutes
What's Inside
Five parts guide the lesson: when to use the Law of Cosines versus the Law of Sines, the formula in three forms plus the angle form, the link to the Pythagorean Theorem with a calculator check, two worked examples (SAS finds a side, SSS finds an angle), and a You Try section. A 2-page answer key is included.
Skill Progression
- Guided practice: Parts A–C, fill-in blanks on when to use the law, the three forms, and the Pythagorean link, with full sentence support.
- Supported practice: Part D, two worked examples with blanks in each step, one SAS and one SSS.
- Independent practice: Part E, four You Try problems, two SAS and two SSS, with work space for each solution.
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. This worksheet targets the Law of Cosines half of the standard. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- During direct instruction: Project the notes and complete Parts A–D together, then assign Part E for independent work.
- After instruction: Use as a review sheet or absent-student catch-up.
Formative tip: while students work Part E, check whether each chooses the correct formula and has the calculator in degree mode. Expect 25–35 minutes.
Who It's For
Students in Grades 10–12 in Geometry, Algebra 2, or Precalculus meeting oblique triangles for the first time. The fill-in format supports students who need note-taking structure, including English learners and students with IEPs. Pair it with a Law of Sines anchor chart for comparing the two methods.
The Law of Cosines Guided Notes worksheet for Grades 10–12 Math supports standard HSG-SRT.D.11, which asks students to apply the Law of Cosines to find unknown sides and angles in non-right triangles. In 2 pages and 30 fill-in items, students learn to choose the Law of Cosines for SAS and SSS triangles, write the formula in three forms, see how it reduces to the Pythagorean Theorem when the angle is 90°, and practice with two worked examples and four independent problems. The structure follows the gradual release of responsibility model described by Fisher & Frey (2014), in which teachers move from modeling to guided practice to independent work. Students round to the nearest tenth and verify results with a calculator in degree mode. A 2-page answer key is included, making the resource suitable for first-lesson instruction, review, or absent-student make-up work in Geometry, Algebra 2, and Precalculus.
