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Aligned Law of Sines & Cosines Worksheet | Grades 10–12 Math
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This worksheet builds the skill of solving real-world triangle problems with the Law of Sines and Law of Cosines. Students sketch and label each situation, choose the correct law, solve, and answer in context with units, practicing how to justify their method.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Laws of Sines and Cosines to solve real-world triangle problems- Skill Focus: Choosing and applying the correct law
- Format: 2 pages · 12 problems · Answer key included · PDF
- Best For: Applied trigonometry practice after direct instruction
- Time: 40–50 minutes
What's Inside
This 2-page worksheet has 12 word problems in four parts: 5 Law of Cosines side problems, 2 Law of Cosines angle problems, 2 Law of Sines problems, and 3 two-step problems using both laws. Each part opens with a worked example and a sketch-and-label prompt. A 2-page answer key is included.
Skill Progression
- Guided practice: Part A, 5 side-finding problems with a worked example and a full-precision reminder.
- Supported practice: Parts B and C, 4 angle and Law of Sines problems, each part with a worked example.
- Independent practice: Part D, 3 two-step problems where students choose the law for each step.
This follows gradual release: I Do (worked examples), We Do (Parts A–C), You Do (Part D).
Standards Alignment
HSG-SRT.D.11 — Understand and apply the Law of Sines and Law of Cosines to find unknown measurements in right and non-right triangles, such as surveying problems and resultant forces. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- During instruction: Use Parts A–C as guided class practice after teaching both laws.
- After instruction: Assign Part D as an exit task or a review before an assessment.
Formative tip: as students work, check whether they sketch first and name the given information (two sides and the included angle, or an angle with its opposite side) before choosing a law. Expect 40–50 minutes for the full set.
Who It's For
Designed for Grades 10–12 students in Geometry, Algebra II, or Precalculus. Students who need support can complete Parts A and B using the worked examples; early finishers can explain in writing why each law was chosen. Pair it with a one-page anchor chart showing when to use each law.
Standard HSG-SRT.D.11 asks students to apply the Law of Sines and the Law of Cosines to find unknown sides and angles in applied triangle problems. This Grades 10–12 math worksheet provides 12 word problems across 2 pages, organized in four parts: finding a side with the Law of Cosines, finding an angle with the Law of Cosines, using the Law of Sines, and combining both laws in two-step problems. Students sketch and label each triangle, select the appropriate law, keep full calculator precision, and round only the final answer with units. The structure reflects the gradual release model described by Fisher & Frey (2014), which moves learners from modeled examples to guided work and then to independent application. A 2-page answer key supports quick checking and feedback. Teachers can assign it as classwork, homework, or review.
