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Here is the problem: A right triangle has legs 20 and 21. Find the hypotenuse.

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Find the hypotenuse of a right triangle from its two legs.

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Write the Pythagorean theorem. The hypotenuse c is the side opposite the right angle and is always the longest side.

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Substitute the legs and square them.

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Take the positive square root. Lengths are positive, so only the positive root is used.

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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 c equals 29; area equals 210; perimeter approximately 70; angles approximately 43.602819°, 46.397181°, 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 841 and c squared equals 841, which agree.

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(20, 21, 29) is a Pythagorean triple: all three sides are whole numbers.

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Angle sum: 90° plus 43.602819° plus 46.397181° equals 180°.