Special right triangles. Game on.

Special right triangles is a grade 10 math skill aligned to Common Core standard HSG.SRT.C.8: use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 23 special right triangles problems our math games drill.

CCSS HSG.SRT.C.823 questions in the bank
Kickoff

8 plays. No signup.

Warm-upeasy

In a 3030-6060-9090 triangle the hypotenuse is 1414. What is the short leg?

The short leg is half the hypotenuse: 142=7\dfrac{14}{2} = 7.

Mid-gameeasy

In a 4545-4545-9090 triangle one leg is 1212. What is the other leg?

Both legs of a 4545-4545-9090 triangle are equal, so the other leg is 1212.

Mid-gameeasy

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, a leg is 9.9\textsf{.} What is the hypotenuse?

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, the hypotenuse is a leg times 2:\sqrt{2}\textsf{:} 92.9\sqrt{2}\textsf{.}

Mid-gameeasy

In a 3030-6060-9090 triangle the short leg is 88. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×8=162 \times 8 = 16.

Mid-gameeasy

In a 4545-4545-9090 triangle one leg is 77. What is the other leg?

Both legs of a 4545-4545-9090 triangle are equal, so the other leg is 77.

Mid-gameeasy

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, a leg is 12.12\textsf{.} What is the hypotenuse?

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, the hypotenuse is a leg times 2:\sqrt{2}\textsf{:} 122.12\sqrt{2}\textsf{.}

Mid-gameeasy

In a 3030-6060-9090 triangle the short leg is 33. What is the hypotenuse?

The hypotenuse is twice the short leg: 2×3=62 \times 3 = 6.

Buzzer beatereasy

In a 4545-4545-9090 triangle one leg is 1515. What is the other leg?

Both legs of a 4545-4545-9090 triangle are equal, so the other leg is 1515.

Overtime

15 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover special right triangles:
NAEPSBACSATLEAP 2025NY State Math
Reporting domains for this skill
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathSBAC High School: Concepts and ProceduresNAEP Grade 12: Measurement and GeometryACT Aspire All grades: Preparing for Higher MathATLAS Algebra I: Geometry
More Grade 10 skills
Surface area and volumeRotations, reflections, and translationsRight triangle trig from two ratiosPerimeter and arc lengthMidpoint formulaEquation of a circlePossible coordinates on a circle (SAT)Circle equation translations (ACT/SAT/PSAT 8/9/10)All Grade 10 practice →

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