Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.2

TRIG.115 Choose between the Law of Sines and Law of Cosines Worksheet

Download our free printable Trigonometry Math worksheet on TRIG.115 Choose between the 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.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Choose between the Law of Sines and Law of Cosines Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.115 Choose between the Law of Sines and Law of Cosines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.115 Choose between the Law of Sines and Law of Cosines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select which law of sines or law of cosines is appropriate for given triangle data (ASA, AAS, SAS, SSS, SSA). Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

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

Trigonometry

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 TRIG.115 Choose between the Law of Sines and Law of Cosines skill assessments:

Problem 1Difficulty: Mastery

Which summary accurately separates the usual first-law choices for oblique triangles?

AASA, AAS, and SSA usually start with the Law of Sines; SAS and SSS usually start with the Law of Cosines.

BASA and AAS use the Law of Cosines; SAS, SSS, and SSA use the Law of Sines.

CAll triangle data types start with the Law of Cosines unless the triangle is right.

DAll triangle data types start with the Law of Sines because every side has an opposite angle.

Solution & Explanation:Law of Sines is matched with situations involving angles and an opposite pair, while Law of Cosines is matched with SAS and SSS first steps.

Problem 2Difficulty: Mastery

An oblique triangle problem gives two sides, a non-included angle, and a warning that there may be 0, 1, or 2 possible triangles. Which law tests the possibilities?

ALaw of Sines, because the ambiguous case is tied to SSA data.

BLaw of Cosines, because ambiguity only happens with included angles.

CNeither law, because ambiguous cases cannot be analyzed.

DLaw of Cosines after replacing the non-included angle with 90 degrees.

Solution & Explanation:The 0-1-2 triangle warning is the SSA ambiguous case. It starts with the Law of Sines.

Problem 3Difficulty: Mastery

A problem gives a non-included angle, its opposite side, and another side. Which first choice is best?

ALaw of Sines, because the known opposite pair starts the SSA setup.

BLaw of Cosines, because two side lengths appear in the problem.

CNeither law, because non-included angles cannot be used.

DLaw of Cosines after finding the included angle by subtraction.

Solution & Explanation:A non-included angle with its opposite side and another side is SSA. The Law of Sines is the correct first step.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this TRIG.115 Choose between the Law of Sines and Law of Cosines worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this TRIG.115 Choose between the Law of Sines and Law of Cosines worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice TRIG.115 Choose between the Law of Sines and Law of Cosines online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.115 Choose between the 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 Trigonometry Math students. It aligns with educational standard UTRI.TA.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select which law of sines or law of cosines is appropriate for given triangle data (ASA, AAS, SAS, SSS, SSA). Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.).