Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.2

TRIG.109 Law of Sines and Law of Cosines for general triangles Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.109 Law of Sines and Law of Cosines for general triangles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.109 Law of Sines and Law of Cosines for general triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select which law applies to a given triangle information set and determine the missing side, angle, or area. 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.109 Law of Sines and Law of Cosines for general triangles skill assessments:

Problem 1Difficulty: Mastery
Triangle ABC has A=31 degrees, a=40, and b=65. Two triangles are possible. Using the smaller possible angle B, find the area. Round to the nearest tenth.
Solution & Explanation:The Law of Sines gives the smaller B=56.8 degrees. Then C=180-31-56.8=92.2 degrees, and K=(1/2)(40)(65)sin(C)=1299.1.
Problem 2Difficulty: Mastery
Triangle ABC has a=41, b=52, and c=63. Which setup correctly starts finding angle C?
Acos(C)=(412+522-632)/(2(41)(52))
Bsin(C)/63=sin(41 degrees)/52
CC=180-41-52-63
Dcos(C)=(632+522-412)/(2(63)(52))
Solution & Explanation:Angle C is opposite side c=63 and lies between sides a=41 and b=52. The Law of Cosines setup is cos(C)=(a2+b2-c2)/(2ab).
Problem 3Difficulty: Mastery
Two forces of 24 N and 31 N act with an angle of 35 degrees between them. Find the resultant force magnitude. Round to the nearest tenth.
Solution & Explanation:Use R2=242+312+2(24)(31)cos(35 degrees). The resultant is 52.5 N.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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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 applies to a given triangle information set and determine the missing side, angle, or area. 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.).

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