Free Printable WorksheetMathGeometryMath CurriculumG-MG.A.1

GEO.177 Apply similarity and trigonometry in modeling Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.177 Apply similarity and trigonometry in modeling. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.177 Apply similarity and trigonometry in modeling - Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.1. Skill statement in this prompt cell: Select the correct similarity or trigonometry setup for a modeling situation and determine the requested distance or height. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1; CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c). 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.177 Apply similarity and trigonometry in modeling skill assessments:

Problem 1Difficulty: Mastery

A surveyor stands 120 ft along a road that slopes downward 12 degrees from the base of a tower. From the surveyor's 5 ft eye height, the angle of elevation to the tower top is 36 degrees. Which setup gives the tower height H above its base to the nearest tenth?

AH = 5 + 120tan(36), so H = 92.2 ft

BH = 5 + (120cos(12))tan(36) - 120sin(12), so H = 65.3 ft

CH = (120sin(12))tan(36) + 5, so H = 23.1 ft

DH = 5 + (120cos(12))tan(36) + 120sin(12), so H = 115.2 ft

Solution & Explanation:The horizontal distance is 120cos(12). Because the surveyor is downhill, the tower base is 120sin(12) above the surveyor. Add eye height, line-of-sight rise, and ground elevation difference: H = 115.2 ft.

Problem 2Difficulty: Mastery

For a 68 ft ramp that rises 7 ft, a student uses tan(theta) = 7/68 to find the angle with the ground. Which correction is best?

AUse cos(theta) = 7/68, because 7 ft is adjacent

BKeep tan(theta) = 7/68, because the ramp length is horizontal

CUse sin(theta) = 7/68, because 68 ft is the ramp length, or hypotenuse

DUse tan(theta) = 68/7, because rise goes in the denominator

Solution & Explanation:The 68 ft measurement is the ramp length, which is the hypotenuse, not the horizontal run. The correct setup is sin(theta) = 7/68.

Problem 3Difficulty: Mastery

A person stands 16 m from a building and measures an angle of elevation of 70 degrees to the roof. The person then backs up 10 m, so the horizontal distance is 26 m. Which predicted angle at the new point is correct to the nearest tenth if the building height stays the same?

AFirst h = 16sin(70), then tan(theta) = h/26, so theta = 30.1 degrees

BFirst h = 16tan(70), then tan(theta) = h/26, so theta = 59.4 degrees

CFirst h = 16tan(70), then tan(theta) = 26/h, so theta = 30.6 degrees

DFirst h = 26tan(70), then tan(theta) = h/16, so theta = 77.9 degrees

Solution & Explanation:The original height is h = 16tan(70). From 26 m away, tan(theta) = h/26, which gives theta about 59.4 degrees.

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Frequently Asked Questions

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QHow do I download and print this GEO.177 Apply similarity and trigonometry in modeling worksheet?

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QIs this GEO.177 Apply similarity and trigonometry in modeling 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-MG.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.1. Skill statement in this prompt cell: Select the correct similarity or trigonometry setup for a modeling situation and determine the requested distance or height. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1; CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).