Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.2

TRIG.120 Solve multi step applications involving 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.120 Solve multi step applications involving general triangles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.120 Solve multi-step applications involving general triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select the correct sequence of steps and computations for a multi-step application involving a general triangle. 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.120 Solve multi step applications involving general triangles skill assessments:

Problem 1Difficulty: Mastery

A design review asks which workflow avoids a right-triangle assumption. A student sees sides 36 cm and 28 cm with included angle 73 deg and wants the third side and area. Which response gives the correct method and computations?

AUse the Pythagorean theorem for z and area = 0.5(36)(28) because any two sides can be treated as perpendicular.

BUse Law of Sines first to find z, because two sides and one angle are always enough for a sine ratio.

CUse area = 0.5(36)(28)cos(73) and then set z equal to the area divided by 36.

DDo not assume a right triangle; use Law of Cosines for third side z = 38.6 cm, and use area = 0.5(36)(28)sin(73) = 482.0 square cm.

Solution & Explanation:The included angle is not 90 deg, so the Pythagorean theorem is not justified. SAS data call for Law of Cosines for z and the sine area formula for area.

Problem 2Difficulty: Mastery

An inspector reviews a student's method for an oblique triangular machine plate. A student sees sides 44 mm and 57 mm with included angle 126 deg and wants the third side and area. Which response gives the correct method and computations?

AUse the Pythagorean theorem for z and area = 0.5(44)(57) because any two sides can be treated as perpendicular.

BUse Law of Sines first to find z, because two sides and one angle are always enough for a sine ratio.

CDo not assume a right triangle; use Law of Cosines for third side z = 90.2 mm, and use area = 0.5(44)(57)sin(126) = 1014.5 square mm.

DUse area = 0.5(44)(57)cos(126) and then set z equal to the area divided by 44.

Solution & Explanation:The included angle is not 90 deg, so the Pythagorean theorem is not justified. SAS data call for Law of Cosines for z and the sine area formula for area.

Problem 3Difficulty: Mastery

A marine survey zone uses two range readings and bearings from a lighthouse. From a station, two boundary markers are 6.4 km and 4.9 km away on bearings 072 and 331. Boundary material costs $2500 per km. Which sequence correctly finds the third boundary, area, and material cost?

AUse bearing sum 403 deg as the included angle, then apply Law of Sines to find the third boundary.

BUse the smaller bearing difference, 101 deg; Law of Cosines gives third boundary 8.8 km; area = 0.5(6.4)(4.9)sin(101) = 15.4 square km; material cost is about $50179 using the unrounded third boundary.

CFind the third boundary by adding 6.4+4.9, then use Heron's formula with the angle as a side.

DUse a right-triangle area formula with legs 6.4 and 4.9, then multiply area by $2500.

Solution & Explanation:The bearings determine the included angle, 101 deg. With SAS data, Law of Cosines gives the third side, the sine area formula gives area, and perimeter times rate gives the cost.

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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 the correct sequence of steps and computations for a multi-step application involving a general triangle. 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.).