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Here is the problem: A right triangle has legs 7 and 24. 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 25; area equals 84; perimeter approximately 56; angles approximately 16.260205°, 73.739795°, 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 625 and c squared equals 625, which agree.

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(7, 24, 25) is a Pythagorean triple: all three sides are whole numbers.

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Angle sum: 90° plus 16.260205° plus 73.739795° equals 180°.