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Here is the problem: A right triangle has hypotenuse 17 and one leg 8. Find the other leg.

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Find the missing leg of a right triangle from the other leg and the hypotenuse.

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Rearrange the Pythagorean theorem for a leg.

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Substitute and simplify.

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Take the positive square root.

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Area and perimeter.

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Acute angles. Angle A is opposite leg a and angle B is opposite leg b; the right angle C is 90°.

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So the answer is b equals 15; area equals 60; perimeter approximately 40; angles approximately 28.072487°, 61.927513°, 90°.

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In every right triangle the square on the hypotenuse equals the sum of the squares on the two legs. Knowing any two sides fixes the third, and the angles follow from the tangent ratio.

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Check: a squared plus b squared equals 289 and c squared equals 289, which agree.

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(8, 15, 17) is a Pythagorean triple: all three sides are whole numbers.

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Angle sum: 90° plus 28.072487° plus 61.927513° equals 180°.