Free Printable WorksheetMathTrigonometryMath CurriculumHSG.SRT.B.4

TRIG.17 Use special right triangles as a basis for exact values Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.17 Use special right triangles as a basis for exact values. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.17 Use special right triangles as a basis for exact values - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.B.4. Skill statement in this prompt cell: Select the correct side-length relationship or exact value that comes from a 45-45-90 or 30-60-90 triangle. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.B.4; CCSS HSF.TF.A.3 (+); TEKS §111.42(c)(4)(E); VA T.TT.1b. 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.17 Use special right triangles as a basis for exact values skill assessments:

Problem 1Difficulty: Mastery
In a 45-45-90 triangle, the hypotenuse minus one leg is 5sqrt(2) - 5. What is the leg length?
Solution & Explanation:If the leg is s, the hypotenuse is s sqrt(2), so the difference is s(sqrt(2) - 1). Since the difference is 5(sqrt(2) - 1), s = 5.
Problem 2Difficulty: Mastery
In a 30-60-90 triangle, the longer leg minus the short leg is 4sqrt(3) - 4. What is the short leg?
Solution & Explanation:If the short leg is s, the difference is s sqrt(3) - s = s(sqrt(3) - 1). The given difference is 4(sqrt(3) - 1), so s = 4.
Problem 3Difficulty: Mastery
Which listed exact value is greatest?
Asin(30 degrees) = 1/2
Bcos(45 degrees) = sqrt(2)/2
Csin(60 degrees) = sqrt(3)/2
Dtan(30 degrees) = sqrt(3)/3
Solution & Explanation:Compare the values: 1/2, sqrt(2)/2, sqrt(3)/2, and sqrt(3)/3. The largest is sqrt(3)/2, which is sin(60 degrees).

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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 HSG.SRT.B.4 (Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.B.4. Skill statement in this prompt cell: Select the correct side-length relationship or exact value that comes from a 45-45-90 or 30-60-90 triangle. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.B.4; CCSS HSF.TF.A.3 (+); TEKS §111.42(c)(4)(E); VA T.TT.1b. Use this prompt-provided wording as the supporting standard description for this workflow.).

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