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Printable Law of Cosines Worksheet | Grades 10–12 Math
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This Law of Cosines task card activity helps students find a missing side from two sides and the included angle, find an angle from three sides, and apply both skills to solving triangles and word problems. Twelve cards support stations, scoot, or partner work, and students check results against an answer key.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Law of Cosines to find unknown sides and angles- Skill Focus: Law of Cosines for SAS and SSS triangles
- Format: 3 pages · 12 problems · Answer key included · PDF
- Best For: Stations, scoot, and partner practice
- Time: 25–35 minutes
What's Inside
Three student pages hold 12 task cards in three parts, plus a recording sheet. Parts A and B each open with a worked example and a formula reminder. Part C adds two-step solve-the-triangle cards and two short word problems. Students record every answer in Part D, and a three-page answer key supports self-checking.
Skill Progression
- Guided practice: Part A, 4 SAS cards (find side x) with a worked example and the formula in view.
- Supported practice: Part B, 4 SSS cards (find an angle) with a worked example and an inverse cosine reminder.
- Independent practice: Part C, 4 cards with two-step triangles, a hiker problem, and a garden problem.
The sequence follows gradual release: I Do (worked examples), We Do (partner work), You Do (Part C).
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. These cards focus on the Law of Cosines in SAS and SSS situations, including distance and area-style contexts. This standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- After direct instruction: Post one card at each of 12 stations or run a scoot round, with students recording answers in Part D.
- During partner work: Pairs solve a part together, then compare with the answer key and correct mistakes.
Formative tip: circulate and watch for students who forget the square root in Part A or round before the final step. Expect 25–35 minutes.
Who It's For
Built for Grades 10–12 Geometry, Algebra II, and Trigonometry students who already know basic trigonometric ratios. Students who need support can lean on the worked examples and work in pairs, while ready students can start with Part C. Pair it with an anchor chart showing both Law of Cosines formulas.
HSG-SRT.D.11 asks students to use the Law of Cosines to find unknown measurements in non-right triangles. This Grades 10–12 Math task card activity gives students 12 cards across three parts: four side-finding cards (SAS), four angle-finding cards (SSS), and four two-step or word-problem cards. Each part opens with a worked example, so learners see the formula applied before they try it. Fisher & Frey (2014) describe gradual release of responsibility, moving from modeled work to guided and then independent practice, as a reliable structure for building skill, and the card sequence follows that pattern. Students record answers on a single sheet, rounded to the nearest tenth, and compare them with the three-page answer key for immediate self-checking. The set runs 25 to 35 minutes and works at stations, in scoot, or with partners for focused Law of Cosines practice.
