Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.87

Pre CAL.87 Law of Sines and Law of Cosines Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.87 Law of Sines and Law of Cosines. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.87 Law of Sines and Law of Cosines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.87 Law of Sines and Law of Cosines - Law of Sines and Law of Cosines

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.87 Law of Sines and Law of Cosines skill assessments:

Problem 1Difficulty: Mastery

In triangle ABC, b = 21, c = 17, and angle A = 59°. What is side a (nearest tenth)?

A23.0

B19.0

C15.5

D20.9

Solution & Explanation:Use the Law of Cosines for a side: a² = 21² + 17² − 2(21)(17)cos(59°). Evaluate the right side, take the square root to get a, and round as directed.

Problem 2Difficulty: Mastery

In triangle ABC, angle A = 52°, side a = 9, and side b = 17. What can you conclude?

AExactly one triangle exists

BTwo triangles exist

CNo triangle exists

DThe triangle must be right

Solution & Explanation:Law of Sines would require sin(B) = b·sin(A) ÷ a = 17·sin(52°) ÷ 9 ≈ 1.49. Since this is greater than 1, it is impossible, so no triangle exists.

Problem 3Difficulty: Mastery

In triangle ABC, angle A = 35°, side a = 14, and side b = 18. Two triangles are possible. Which triangle has the larger area?

AThe triangle with acute angle B

BThe triangle with obtuse angle B

CBoth areas are equal

DNeither triangle is possible

Solution & Explanation:Find both triangles via SSA, then compute c for each. Since A is fixed, area = 0.5·b·c·sin(A). The triangle with the larger c has the larger area. Comparing the two solutions shows the acute‑B triangle has the larger area.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this Pre CAL.87 Law of Sines and Law of Cosines worksheet free for teachers and homeschoolers?

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QCan students practice Pre CAL.87 Law of Sines and Law of Cosines online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.87 Law of Sines and Law of Cosines interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.87 (Law of Sines and Law of Cosines).