Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.AM.2

TRIG.34 Compute arc length from radius and central angle Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.34 Compute arc length from radius and central angle. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.34 Compute arc length from radius and central angle - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Select the correct arc length given radius and central angle, including solving for a missing variable when needed. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. 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.34 Compute arc length from radius and central angle skill assessments:

Problem 1Difficulty: Mastery
An arc has radius 40 units and length 30pi units. Which central angle and fraction of a full rotation are correct?
A120 degrees and 1/3
B135 degrees and 3/8
C150 degrees and 5/12
D270 degrees and 3/4
Solution & Explanation:The circumference is 80pi. The arc fraction is 30pi/80pi = 3/8. Then the central angle is (3/8)(360) = 135 degrees.
Problem 2Difficulty: Mastery
An arc length of 10pi cm is formed by radius r and central angle 150 degrees. Another sector with radius r + 6 and central angle 100 degrees has the same arc length. What is r?
Solution & Explanation:Set (150/360)(2pi r) equal to (100/360)(2pi)(r + 6). This simplifies to 5r/6 = 5(r + 6)/9, so r = 12.
Problem 3Difficulty: Mastery
A circular logo has radius 18 cm. The highlighted arc is 2/9 of the circumference. Which central angle and arc length match the arc?
A40 degrees and 4pi cm
B80 degrees and 8pi cm
C90 degrees and 9pi cm
D120 degrees and 12pi cm
Solution & Explanation:A fraction of 2/9 of a full rotation is (2/9)(360) = 80 degrees. The circumference is 36pi, and 2/9 of it is 8pi cm.

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Frequently Asked Questions

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QIs this TRIG.34 Compute arc length from radius and central angle worksheet free for teachers and homeschoolers?

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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.AM.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Select the correct arc length given radius and central angle, including solving for a missing variable when needed. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.).

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