Free Printable WorksheetMathGeometryMath CurriculumG-SRT.C.6-8

GEO.97 Model with right triangle trigonometry Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.97 Model with right triangle trigonometry. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.97 Model with right-triangle trigonometry - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.C.6-8. Skill statement in this prompt cell: Select the diagram and trigonometric equation that matches an application problem and determine the requested distance or angle. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c); CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1. 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.97 Model with right triangle trigonometry skill assessments:

Problem 1Difficulty: Mastery

Two ropes reach the top of a vertical tower from ground anchors on opposite sides. Two anchors are on opposite sides of the vertical object and are 80 m apart. The angles of elevation to the top are 42 deg and 57 deg. Which option shows the correct diagram, equation, and tower height? Round to the nearest tenth.

ADiagram: both stakes are treated as if they are on the same side, with the 57 deg angle at the closer point; Equation: h = x tan(57 deg), h = (x + 80) tan(42 deg); tower height = 173.5 m

BDiagram: the angle labels are used with sine instead of tangent; Equation: h/sin(42 deg) + h/sin(57 deg) = 80; tower height = 29.8 m

CDiagram: the horizontal legs are multiplied by tangent after splitting the distance evenly; Equation: h = (80/2)tan(42 deg); tower height = 36.0 m

DDiagram: stakes are on opposite sides, so the two horizontal legs add to 80 m; Equation: h/tan(42 deg) + h/tan(57 deg) = 80; tower height = 45.5 m

Solution & Explanation:Let h be the height. The left horizontal distance is h/tan(42 deg), and the right horizontal distance is h/tan(57 deg). These distances add to 80 m, so h = 45.5 m.

Problem 2Difficulty: Mastery

An escalator rises 18 ft and makes a 26 deg angle with the floor. Which option shows the correct right-triangle diagram setup, trigonometric equation, and horizontal floor distance? Round to the nearest tenth.

ADiagram: Diagram treats horizontal floor distance as the opposite side and vertical rise as the hypotenuse; Equation: sin(26 deg) = x/18; horizontal floor distance = 7.9 ft

BDiagram: Diagram treats vertical rise as the opposite side and horizontal floor distance as the hypotenuse; Equation: sin(26 deg) = 18/x; horizontal floor distance = 41.1 ft

CDiagram: Diagram treats vertical rise as the opposite side and horizontal floor distance as the adjacent; Equation: tan(26 deg) = 18/x; horizontal floor distance = 36.9 ft

DDiagram: Diagram treats horizontal floor distance as the adjacent side and vertical rise as the hypotenuse; Equation: cos(26 deg) = x/18; horizontal floor distance = 16.2 ft

Solution & Explanation:In the matching right triangle, horizontal floor distance is the adjacent side relative to the 26 deg angle, and vertical rise is the opposite side. So tan(26 deg) = 18/x, which gives x = 36.9 ft. Therefore, horizontal floor distance = 36.9 ft.

Problem 3Difficulty: Mastery

A bridge cable attaches to the deck 120 m from a tower and makes a 31 deg angle with the deck. Which option shows the correct right-triangle diagram setup, trigonometric equation, and height reached on the tower? Round to the nearest tenth.

ADiagram: Diagram treats tower height reached as the opposite side and deck distance as the hypotenuse; Equation: sin(31 deg) = x/120; height reached on the tower = 61.8 m

BDiagram: Diagram treats tower height reached as the opposite side and deck distance as the adjacent; Equation: tan(31 deg) = x/120; height reached on the tower = 72.1 m

CDiagram: Diagram treats deck distance as the opposite side and tower height reached as the hypotenuse; Equation: sin(31 deg) = 120/x; height reached on the tower = 233.0 m

DDiagram: Diagram treats tower height reached as the adjacent side and deck distance as the hypotenuse; Equation: cos(31 deg) = x/120; height reached on the tower = 102.9 m

Solution & Explanation:In the matching right triangle, tower height reached is the opposite side relative to the 31 deg angle, and deck distance is the adjacent side. So tan(31 deg) = x/120, which gives x = 72.1 m. Therefore, height reached on the tower = 72.1 m.

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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 Geometry Math students. It aligns with educational standard G-SRT.C.6-8 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.C.6-8. Skill statement in this prompt cell: Select the diagram and trigonometric equation that matches an application problem and determine the requested distance or angle. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c); CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1. Use this prompt-provided wording as the supporting standard description for this workflow.).