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Here is the problem: A right triangle has hypotenuse 15 and one leg 9. 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 12; area equals 54; perimeter approximately 36; angles approximately 36.869898°, 53.130102°, 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 225 and c squared equals 225, which agree.

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(9, 12, 15) is a Pythagorean triple: all three sides are whole numbers.

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Angle sum: 90° plus 36.869898° plus 53.130102° equals 180°.