Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.1

TRIG.108 Right triangle trigonometry in applied problems Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.108 Right triangle trigonometry in applied problems. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.108 Right-triangle trigonometry in applied problems - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct trigonometric ratio or inverse-trigonometric method to solve a right-triangle application and identify the correctly rounded answer with units. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-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

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.108 Right triangle trigonometry in applied problems skill assessments:

Problem 1Difficulty: Mastery
A survey drone flies 25 kilometers on a straight path and ends 18 kilometers east of its starting point. What angle north of east was the path, to the nearest tenth of a degree?
Solution & Explanation:The east component is adjacent to the angle and the flight path is the hypotenuse. Use theta=arccos(18/25)=43.9 degrees.
Problem 2Difficulty: Mastery
An airplane climbs at an 8-degree angle for 4.5 minutes while traveling 160 miles per hour along its flight path. Which result gives its altitude gain to the nearest foot?
A160(4.5/60)tan(8 degrees)*5280=8905 ft
B160(4.5/60)cos(8 degrees)*5280=62743 ft
C160(4.5/60)sin(8 degrees)*5280=8818 ft
D160(4.5)sin(8 degrees)*5280=529080 ft
Solution & Explanation:The plane travels 160*(4.5/60)=12 miles along the hypotenuse. Altitude gain is 12 sin(8 degrees) miles, or 8818 feet.
Problem 3Difficulty: Mastery
An observer sees a drone at a 33-degree angle of elevation. The drone then climbs vertically 40 meters without moving horizontally, and the new angle of elevation is 45 degrees. What was the drone's initial altitude, to the nearest tenth of a meter?
Solution & Explanation:Let h be the initial altitude and x be the horizontal distance. Since the new angle is 45 degrees, x=h+40. Also h/x=tan(33 degrees). Solve h/(h+40)=tan(33 degrees), giving h=74.1 meters.

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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.1 (Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct trigonometric ratio or inverse-trigonometric method to solve a right-triangle application and identify the correctly rounded answer with units. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-d. Use this prompt-provided wording as the supporting standard description for this workflow.).

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