Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.1

TRIG.113 Solve problems involving angles of elevation and depression Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.113 Solve problems involving angles of elevation and depression. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.113 Solve problems involving angles of elevation and depression - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct diagram and equation for an elevation or depression problem and determine the unknown distance or height. 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.113 Solve problems involving angles of elevation and depression skill assessments:

Problem 1Difficulty: Mastery
A sensor on a 40-meter tower sees the base of a second tower at a 22 degree angle of depression and the top of the second tower at an 18 degree angle of elevation. What is the height of the second tower? Round to the nearest tenth.
Solution & Explanation:The horizontal distance is 40/tan(22 degrees)=99.0. The top is 99.0*tan(18 degrees) above the sensor, so the second tower is 72.2 meters tall.
Problem 2Difficulty: Mastery
An observer with eye level 1.7 meters measures a tower from two points 36 meters apart. The farther angle of elevation is 27 degrees and the closer angle is 46 degrees. Which complete model and total height H are correct?
AH=1.7+x*tan(46 degrees), where x*tan(46 degrees)=(x+36)*tan(27 degrees); H=37.8 m.
BH=1.7+x*tan(27 degrees), where x*tan(27 degrees)=(x+36)*tan(46 degrees); H=19.5 m.
CH=1.7+36*tan(46 degrees)+36*tan(27 degrees); H=57.3 m.
DH=1.7+x/tan(46 degrees), where x/tan(46 degrees)=(x+36)/tan(27 degrees); H=35.4 m.
Solution & Explanation:The larger angle is at the closer point. The height above eye level is x*tan(46 degrees) at the closer point and (x+36)*tan(27 degrees) at the farther point, then add eye level.
Problem 3Difficulty: Mastery
A stadium seat is 18 meters above field level. The angle of depression to the near sideline is 11 degrees and to the far sideline is 6 degrees. How wide is the field between those sidelines from this viewpoint? Round to the nearest tenth.
Solution & Explanation:Distances to the sidelines are 18/tan(11 degrees) and 18/tan(6 degrees). The field width between them is the difference, 78.7 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 diagram and equation for an elevation or depression problem and determine the unknown distance or height. 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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