Pythagorean theorem in context (SAT/ACT). Game on.

Pythagorean theorem in context (SAT/ACT) is a grade 8 math skill aligned to Common Core standard 8.G.B.7: apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Below are 4 practice questions with answers and step-by-step explanations, drawn from the 6 pythagorean theorem in context (sat/act) problems our math games drill.

CCSS 8.G.B.76 questions in the bank
Kickoff

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Warm-upeasy

Jordan walks 88 blocks east and then 1515 blocks north. How many blocks from the starting point is Jordan, measured in a straight line?

The walk forms the legs of a right triangle: 82+152=64+225=289=17\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17 blocks.

Mid-gameeasy

A 2626-meter guy wire runs from the top of a pole to a stake 2424 meters from the pole's base. How tall is the pole?

The wire is the hypotenuse: 262−242=676−576=10026^{2} - 24^{2} = 676 - 576 = 100, so the pole is 100=10\sqrt{100} = 10 meters tall.

Mid-gameeasy

A wheelchair ramp rises 55 feet over a horizontal distance of 1212 feet. What is the length of the ramp?

The ramp is the hypotenuse of a right triangle with legs 55 and 1212: 52+122=25+144=169=13\sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13 feet.

Buzzer beatereasy

A kite string is 2525 meters long and is staked 77 meters from a point on the ground directly below the kite. How high is the kite?

The string is the hypotenuse: 252−72=625−49=57625^{2} - 7^{2} = 625 - 49 = 576, so the height is 576=24\sqrt{576} = 24 meters.

Overtime

2 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 pythagorean theorem in context (sat/act):
NAEPSBACPSAT 8/9SC READYNC EOG/EOC
Reporting domains for this skill
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathSTAAR Grade 8: Geometry and MeasurementMAP Growth Math 6+: Geometryi-Ready Grade 8: GeometrySBAC Grade 8: Concepts and Procedures
More Grade 8 skills
Linear Algebra Basics: SystemsTwo-way tablesInterpreting linear parametersLinear coefficient interpretations (SAT/PSAT 8/9/10)Pythagorean theoremRectangle diagonal from area (ACT)Linear functions with an unknown constantFinding a missing side with the Pythagorean theoremAll Grade 8 practice →

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