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Printable Sines vs Cosines Worksheet | Grades 10-12 Math
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This worksheet teaches students to decide between the Law of Sines and the Law of Cosines before they calculate anything. Learners name the triangle case, choose the law, solve for the unknown side or angle, and explain why the wrong law fails. That decision step is often skipped in trigonometry units.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Choose and apply the correct law to find unknown sides and angles- Skill Focus: Choosing between Law of Sines and Law of Cosines
- Format: 3 pages · 30 problems · Answer key included · PDF
- Best For: Mixed review after teaching both laws
- Time: 40–50 minutes
What's Inside
The worksheet has three parts across 3 pages. Part A asks students to sketch each triangle, name the case, and pick a law without solving. Part B is multi-step solving, rounded to the nearest tenth. Part C requires written explanations. Each part opens with a worked example. A 3-page answer key gives final values and model explanations.
Skill Progression
- Guided practice (Part A): Students sketch, name the case (SAS, SSS, ASA, AAS, SSA), and choose a law, supported by a worked SAS example. No calculation.
- Supported practice (Part B): Students solve for sides and angles, guided by a worked AAS example and rounding rules. Every SSA triangle has exactly one solution.
- Independent practice (Part C): Students explain in complete sentences why the Law of Sines cannot start a given triangle.
The order 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 standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- After direct instruction: Assign Part A as a class warm-up once both laws have been taught, then let students finish Parts B and C independently.
- Before a unit test: Assign all three parts as a mixed review or homework set.
Formative check: while students work Part A, watch whether they look for a known angle with its opposite side before choosing a law. Expect 40–50 minutes in total.
Who It's For
Built for Grades 10–12 students in Geometry, Algebra II, or Precalculus who have met both laws and tend to mix them up. Students needing support can focus on Part A and the worked examples, while Part C stretches stronger students. Pair it with a one-page anchor chart of the five triangle cases.
The Law of Sines and Law of Cosines Mixed Practice worksheet supports CCSS HSG-SRT.D.11, in which students apply both laws to find unknown measurements in non-right triangles. Its core skill is case recognition: naming SAS, SSS, ASA, AAS, or SSA, then selecting the law that fits the known parts and solving to the nearest tenth. The 30-problem, 3-page resource moves from classifying triangles without solving, to computing sides and angles, to written explanations of why one law fails. This sequence reflects the gradual release of responsibility model described by Fisher & Frey (2014), in which teacher modeling gives way to guided and then independent work. A three-page answer key lets teachers check both numerical results and reasoning. It suits Grades 10–12 geometry, Algebra II, and trigonometry classes as mixed review, homework, or a quiz-prep session.
