# Triangles and the Pythagorean Theorem: Finding the Hypotenuse

## How do we determine the length of the hypotenuse in a right triangle using the Pythagorean theorem?

We have a right triangle with side lengths:

- Opposite = 5.7 cm
- Adjacent = 3.2 cm

## Calculation of the hypotenuse:

Using the Pythagorean theorem, we have:

Hypotenuse^2 = Opposite^2 + Adjacent^2

Plugging in the values:

Hypotenuse^2 = 3.2^2 + 5.7^2

Evaluating the sum:

Hypotenuse^2 = 42.73

Taking the square root of both sides:

Hypotenuse = 6.5 cm

Therefore, the hypotenuse of the triangle is 6.5 cm.

The Pythagorean theorem is a fundamental concept in geometry that allows us to find the lengths of the sides of a right triangle. By squaring and summing the lengths of the two shorter sides, we can then take the square root to find the length of the hypotenuse. In this case, where the Opposite side is 5.7 cm and the Adjacent side is 3.2 cm, we apply the theorem to determine that the hypotenuse of the triangle is 6.5 cm.