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Printable Law of Cosines SAS Worksheet | Grade 10–12 Math
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This worksheet teaches students to find a missing side of a triangle with the Law of Cosines when two sides and the included angle are known. Learners move from writing the equation, to solving with calculator precision, to checking whether a triangle truly fits the SAS case.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Law of Cosines to find unknown sides of non-right triangles- Skill Focus: Finding a missing side from two sides and the included angle (SAS)
- Format: 2 pages · 20 problems · Answer key included · PDF
- Best For: Introductory Law of Cosines practice
- Time: 25–35 minutes
What's Inside
Two pages of student work include a worked example in every part. Part A has 4 set-up-only items, Part B has 12 solve-for-the-side items rounded to the nearest tenth, and Part C has 4 figure-based items where students decide whether the angle is included. A 2-page answer key is provided.
Skill Progression
- Guided practice: 4 set-up items. Students substitute values into the formula without solving, with a worked example as a model.
- Supported practice: 12 solving problems with a worked example and a reminder to keep full calculator precision.
- Independent practice: 4 figure items. Students decide SAS or NOT SAS before calculating.
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. Here students apply the Law of Cosines to SAS triangles. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
Assign it after direct instruction as guided classwork, or use Part A alone as a warm-up before the full lesson. Part C works well as an exit check. While students work, watch whether they pair the angle with its opposite side, since that catches most errors. Expect 25–35 minutes.
Who It's For
Built for Grades 10–12 students in Geometry, Algebra II, or Precalculus who are meeting the Law of Cosines for the first time. Part A supports students who need more structure, while Part C stretches stronger students. Pair it with an anchor chart showing how sides and opposite angles are labeled.
HSG-SRT.D.11 asks students to apply the Law of Cosines to find unknown measurements in non-right triangles. This Grade 10–12 Math worksheet focuses on one case: finding a missing side when two sides and the included angle are known (SAS). Its 20 problems move from writing the equation, to solving with full calculator precision and rounding to the nearest tenth, to deciding whether a figure is really SAS. This structure reflects the gradual release model described by Fisher & Frey (2014), in which teachers shift responsibility from modeled examples to supported practice and then to independent work. The two-page format includes worked examples in each part and a two-page answer key. Teachers can use the worksheet as classwork after direct instruction, as a formative check, or as targeted review before applying the Law of Cosines to surveying and navigation problems.
