Free Printable WorksheetMathGeometryMath CurriculumG-SRT.D.9-11 (+)

GEO.99 Law of Sines Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.99 Law of Sines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.99 Law of Sines - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.D.9-11 (+). Skill statement in this prompt cell: Select the correct Law of Sines proportion and determine an unknown side length or angle measure in a triangle. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.D.9-11 (+); NY HS Plus; MA G-SRT.D (+). 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

Geometry

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 GEO.99 Law of Sines skill assessments:

Problem 1Difficulty: Mastery

A final review problem asks students to set up the proportion before checking for a valid angle. In triangle LMO, side o is opposite angle O, and side m is opposite the 101-degree angle. Side o = 49 meters and side m = 85 meters. Which choice gives a correct Law of Sines proportion and the measure of angle O?

Asin(O)/49 = sin(101 degrees)/85; O approximately 34.5 degrees

Bsin(O)/85 = sin(101 degrees)/49; O approximately 113.0 degrees

Csin(O)/49 = sin(101 degrees)/85; O approximately 145.5 degrees

D49/sin(O) = 85/sin(101 degrees); O approximately 66.5 degrees

Solution & Explanation:Use the ratio of each side to the sine of its opposite angle: sin(O)/49 = sin(101 degrees)/85. Then sin(O) = 49*sin(101 degrees)/85, so O is approximately 34.5 degrees. The supplement is not a valid second angle for this triangle because it would make the angle sum exceed 180 degrees.

Problem 2Difficulty: Mastery

A harbor map has a large angle at the first observation point. Points A, D, and E form a triangle. The baseline AD is 205 meters, angle A = 117 degrees, and angle D = 31 degrees. Which choice correctly uses the Law of Sines to find DE?

ADE/sin(32 degrees) = 205/sin(117 degrees); DE approximately 121.9 meters

BDE/sin(117 degrees) = 205/sin(32 degrees); DE approximately 344.7 meters

CDE/sin(31 degrees) = 205/sin(32 degrees); DE approximately 199.2 meters

DDE/sin(117 degrees) = 205/sin(31 degrees); DE approximately 354.6 meters

Solution & Explanation:The third angle is E = 180 - 117 - 31 = 32 degrees. Segment AD is opposite angle E, and DE is opposite the 117-degree angle. Thus DE/sin(117 degrees) = 205/sin(32 degrees), so DE is about 344.7 meters.

Problem 3Difficulty: Mastery

Two triangular roof sections are compared for material estimates. Two separate triangles are measured. In the first, the baseline is 54 feet, the two base angles are 72 degrees and 38 degrees, and rafter 1 is opposite the 38-degree angle. In the second, the baseline is 61 feet, the two base angles are 43 degrees and 82 degrees, and rafter 2 is opposite the 82-degree angle. Which choice gives both Law of Sines results?

Arafter 1 approximately 82.4 feet and rafter 2 approximately 50.5 feet

Brafter 1 approximately 54.7 feet and rafter 2 approximately 50.8 feet

Crafter 1 approximately 35.4 feet and rafter 2 approximately 73.7 feet

DBoth distances are equal because both triangles use a baseline and two angles

Solution & Explanation:For the first triangle, the third angle is 70 degrees, so rafter 1/sin(38 degrees) = 54/sin(70 degrees), giving 35.4 feet. For the second, the third angle is 55 degrees, so rafter 2/sin(82 degrees) = 61/sin(55 degrees), giving 73.7 feet.

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Frequently Asked Questions

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QIs this GEO.99 Law of Sines 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 Geometry Math students. It aligns with educational standard G-SRT.D.9-11 (+) (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.D.9-11 (+). Skill statement in this prompt cell: Select the correct Law of Sines proportion and determine an unknown side length or angle measure in a triangle. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.D.9-11 (+); NY HS Plus; MA G-SRT.D (+). Use this prompt-provided wording as the supporting standard description for this workflow.).