15 questions
11th - 11th Grade
Mathematics
PreCal - Laws of Sine & Cosine Practice is a free printable Grade 11 mathematics worksheet that helps students choose and apply the Law of Sines and Law of Cosines in non-right-triangle problems. Across 15 items, students identify the appropriate law, find missing angles and side lengths, solve real-world distance situations, and determine whether an SSA setup produces zero, one, or two triangles. The worksheet also includes fill-in-the-blank problems requiring answers rounded to the nearest tenth with units, a dropdown item for solving multiple parts of a triangle, and area problems using triangle measurements. Students apply their reasoning to find a largest angle, calculate area, and complete an oblique-triangle solution rather than simply recalling formulas. It is suitable for guided practice, independent review, or assessment, and includes a complete answer key for efficient checking.
Worksheet settings
Font size
WorksheetsAnswer Key,
,
This Grade 11 worksheet uses 11 multiple-choice questions, 3 fill-in-the-blank problems, and 1 dropdown item to practice selecting and applying the Law of Sines or Law of Cosines. Students solve for missing sides and angles, analyze the ambiguous SSA case for zero or two triangles, complete an oblique-triangle solution, and calculate triangle area, including applied distance problems that require rounding and units.
Begin by reviewing which known side-angle arrangements support the Law of Sines and which information supports the Law of Cosines, then use the worksheet’s initial “Which Law would you use?” items as a sorting discussion. After students justify their choices, have them work through the distance, missing-side, and missing-angle problems and explain how the given measurements led to each law. Finish with the SSA items to introduce why one setup can produce zero, one, or two triangles.
Watch for students choosing a law without matching it to the given side-angle information, reversing corresponding sides and angles, or using the wrong value when solving for a missing measurement. In the SSA questions, students may overlook the possibility of two triangles or conclude that a triangle exists when the measurements are impossible. Also check the fill-in responses for nearest-tenth rounding and required units, and the area questions for using the included angle correctly.
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the law selections, numerical solutions, triangle counts, and area answers. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.
Use the worksheet’s Advanced Settings to adjust font spacing or font size so the law-selection prompts, numerical choices, and multi-part triangle-solving item are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the trigonometry directions and answer prompts.
Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
