Pythagorean Theorem for Finding Height of a Triangle | Calculate Hypotenuse

The Pythagorean Theorem is one of the most fundamental principles in mathematics. It describes the relationship between the sides of a right triangle, which is a triangle with a 90-degree angle. In simple terms, the theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side, also known as the hypotenuse.

The Formula and Application of Pythagorean Theorem

The Pythagorean Theorem can be expressed in the formula:

a² + b² = c²

where:

• a and b: the lengths of the two shorter sides of the triangle
• c: the length of the hypotenuse

For example, if a right triangle has a base of 6 cm and a height of 8 cm, we can use the Pythagorean Theorem to find the length of the hypotenuse:

a² + b² = c²

6² + 8² = c²

36 + 64 = c²

100 = c²

c = sqrt(100) = 10 cm

This means that the hypotenuse of the triangle is 10 cm long.

Units of Measurement

When using the Pythagorean Theorem, it's important to make sure that the units of measurement are consistent. For example, if the shorter sides of a right triangle are measured in feet, then the hypotenuse must also be expressed in feet. Similarly, if the triangle's height is measured in centimeters, the other sides must be measured in centimeters as well.

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