Calculating the Length of the Hypotenuse in a Right Triangle

Understanding how to calculate the hypotenuse of a right triangle is a fundamental skill in geometry. The hypotenuse is the longest side of a right triangle and is opposite the right angle. In this article, we will explore a specific example: a right triangle with legs of 8 units and 15 units. We will utilize the Pythagorean Theorem to determine the hypotenuse's length.

The Pythagorean Theorem in Action

The Pythagorean Theorem is a mathematical principle that establishes a relationship between the lengths of the sides of a right triangle. The theorem is stated as follows:

c2 a2 b2

This formula can be rearranged to solve for the hypotenuse:

c √(a2 b2)

Example: Calculating the Hypotenuse

Consider a right triangle with legs of 8 units and 15 units. To find the length of the hypotenuse, we can follow these steps:

Identify the lengths of the legs: a 8 units b 15 units Substitute the values into the Pythagorean Theorem: c2 82 152 Calculate the squares of the legs: 82 64 152 225 Add the squares of the legs: 64 225 289 Take the square root of the sum to find the hypotenuse: c √289 17 units

Additional Examples and Applications

The same process can be applied to other right triangles, regardless of the lengths of their legs. Here are a few more examples:

Example 1: A right triangle with legs of 8 units and 15 units:

c2 82 152 c2 64 225 c2 289 c √289 17 units

Example 2: A right triangle with legs of 8 miles and 15 miles:

c2 82 152 c2 64 225 c2 289 c √289 17 miles

Conclusion

The Pythagorean Theorem is a powerful tool for determining the length of the hypotenuse in a right triangle. By following the steps outlined in this article, you can calculate the hypotenuse for any right triangle, regardless of the lengths of its legs. Whether you're working on a geometry problem or applying the theorem to real-world situations, the Pythagorean Theorem remains an essential concept in mathematics.