Special right triangle sides (ACT). Game on.

Special right triangle sides (ACT) is a grade 12 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 15 special right triangle sides (act) problems our math games drill.

CCSS HSG.SRT.C.815 questions in the bank
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Warm-upeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is 6.6\textsf{.} What is the hypotenuse?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is twice the short leg: 2×6=12.2 \times 6 = 12\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is 14.14\textsf{.} What is the short leg?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is half the hypotenuse: 142=7.\dfrac{14}{2} = 7\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is 9.9\textsf{.} What is the hypotenuse?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is twice the short leg: 2×9=18.2 \times 9 = 18\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is 7.7\textsf{.} What is the hypotenuse?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is twice the short leg: 2×7=14.2 \times 7 = 14\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is 16.16\textsf{.} What is the short leg?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is half the hypotenuse: 162=8.\dfrac{16}{2} = 8\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is 10.10\textsf{.} What is the hypotenuse?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is twice the short leg: 2×10=20.2 \times 10 = 20\textsf{.}

Mid-gameeasy

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the hypotenuse is 22.22\textsf{.} What is the short leg?

In a 30∘30^{\circ}-60∘60^{\circ}-90∘90^{\circ} triangle, the short leg is half the hypotenuse: 222=11.\dfrac{22}{2} = 11\textsf{.}

Buzzer beatereasy

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, the hypotenuse is 52.5\sqrt{2}\textsf{.} What is each leg?

In a 45∘45^{\circ}-45∘45^{\circ}-90∘90^{\circ} triangle, each leg is the hypotenuse divided by 2:\sqrt{2}\textsf{:} 522=5.\dfrac{5\sqrt{2}}{\sqrt{2}} = 5\textsf{.}

Overtime

7 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 triangle sides (act):
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 12 skills
Convergence testsCalculus application formulasDegree-radian conversionLaw of sines and cosinesInverse trig domain and rangeMaclaurin seriesPolar and rectangular conversionSpecial limitsAll Grade 12 practice →

Drill it inside a game.

The free placement test finds your level, then every match serves special right triangle sides (act) questions at exactly the right difficulty.