Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.2

TRIG.118 Analyze the ambiguous case for the Law of Sines Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.118 Analyze the ambiguous case for the Law of Sines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.118 Analyze the ambiguous case for the Law of Sines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select whether SSA yields zero, one, or two triangles and identify the valid solution or solutions. 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.118 Analyze the ambiguous case for the Law of Sines skill assessments:

Problem 1Difficulty: Mastery

In triangle MNP, side m is opposite angle M, side n is opposite angle N, and side p is opposite angle P. Given angle M = 46 deg, side m = 9, and side n = 12, A classmate says angle N could be 73.6 deg or 106.4 deg because sine has two related angles. Which response correctly analyzes the claim?

AZero triangles; no valid value of angle N

BOne triangle; angle N = 73.6 deg

COne triangle; angle N = 106.4 deg

DTwo triangles; angle N = 73.6 deg or 106.4 deg

Solution & Explanation:Use sin(N) = 12 sin(46 deg)/9 = 0.959. The sine value gives N = 73.6 deg or 106.4 deg. Both leave positive third angles (60.4 deg and 27.6 deg), so there are two triangles.

Problem 2Difficulty: Mastery

In triangle GHI, side g is opposite angle G, side h is opposite angle H, and side i is opposite angle I. Given angle G = 39 deg, side g = 8, and side h = 13, find the valid outcome and the possible length(s) of side i. Round to the nearest tenth.

ATwo triangles; side i = 7.0 or 10.0

BOne triangle; side i = 10.0

COne triangle; side i = 7.0

DZero triangles; no valid length of side i

Solution & Explanation:Use the Law of Sines: sin(H) = h sin(G)/g = 13 sin(39 deg)/8 = 1.023. Because this is greater than 1, no angle H exists, so the SSA data make zero triangles.

Problem 3Difficulty: Mastery

In triangle JKL, side j is opposite angle J, side k is opposite angle K, and side l is opposite angle L. Given angle J = 112 deg, side j = 20, and side k = 12, which option gives the complete set of remaining-angle solutions? Round angles to the nearest tenth.

ATwo triangles; (K, L) = (33.8 deg, 34.2 deg) or (58.0 deg, 10.0 deg)

BOne triangle; (K, L) = (33.8 deg, 34.2 deg)

COne triangle; (K, L) = (58.0 deg, 10.0 deg)

DZero triangles; no valid angle pair (K, L)

Solution & Explanation:Use sin(K) = 12 sin(112 deg)/20 = 0.556. The valid angle is K = 33.8 deg. The supplement 146.2 deg would make J + K = 258.2 deg, leaving no positive third angle, so only one triangle works.

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Frequently Asked Questions

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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 whether SSA yields zero, one, or two triangles and identify the valid solution or solutions. 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.).