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Pythagorean theorem is a relation between the three sides of a right triangle. The three sides are two cathetus and a hypotenuse.

Pythagorean theorem definition. In any right triangle, the sum of the squares of the lengths of the cathetus is equal to the square of the length of the hypotenuse.

If we note with c - the hypotenuse and a, b the cathetus. Then the Pythagorean theorem can be written in the following form c² = a² + b².

Abbreviations: A - area, AB - cathetus, AC - cathetus, BC - hypotenuse and AD - height.

1. A right triangle ABC has the cathetus AB = 3 cm and the hypotenuse BC = 5 cm. Calculate the length of the AC cathetus.

BC^{2} = AB^{2} + AC^{2}

AC^{2} = BC^{2} - AB^{2}

AC^{2} = 25 - 9

AC = √16

AC = 4 cm

2. A right triangle ABC has the cathetus AB = 3 cm and AC = 4 cm. Calculate the length of the hypotenuse BC.

BC^{2} = AB^{2} + AC^{2}

BC^{2} = 9 + 16

BC = √25

BC = 5 cm

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