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Here is the problem: A right triangle has hypotenuse 10 and one leg 7. 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 the square root of 51 approximately 7.141428429; area equals 24.9949995; perimeter approximately 24.14142843; angles approximately 44.427004°, 45.572996°, 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 100 and c squared equals 100, which agree.

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Angle sum: 90° plus 44.427004° plus 45.572996° equals 180°.