Right Triangle Calculator: Pythagorean Theorem Solver

What is a Right Triangle?

A right triangle is a type of triangle that has one angle measuring 90 degrees. The side opposite this right angle is called the hypotenuse, and the other two sides are referred to as the legs of the triangle.

Formula

In a right triangle, the relationship between the lengths of the sides is given by the Pythagorean theorem:

\[c^2 = a^2 + b^2\]

where:

• \(a\) is the length of one leg
• \(b\) is the length of the other leg
• \(c\) is the length of the hypotenuse

Calculation Steps

Let's calculate the hypotenuse for a right triangle with legs \(a = 3\) units and \(b = 4\) units:

1. Formula: \[c^2 = a^2 + b^2\]
2. Substitute the values: \[c^2 = 3^2 + 4^2\]
3. Calculate: \[c^2 = 9 + 16\] \[c^2 = 25\] \[c = \sqrt{25}\] \[c = 5\]

Example

For a right triangle with legs \(a = 3\) units and \(b = 4\) units, the hypotenuse \(c\) is 5 units.

Visual Representation

This diagram illustrates the right triangle with the calculated dimensions.