A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. The side opposite this 90-degree angle is called the hypotenuse, which is the longest side of the right triangle. To calculate the hypotenuse, you can use the Pythagorean theorem.

In this article, we will provide a step-by-step guide on how to calculate the hypotenuse of a right triangle using the Pythagorean theorem.

Step 1: Understand the Pythagorean Theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Mathematically, it can be expressed as:

c^2 = a^2 + b^2

Step 2: Identify and Label Triangle Sides

Identify the two shorter sides of your right triangle (a and b) and label them accordingly. These are called legs, which form the 90-degree angle.

Step 3: Calculate Squares of Sides

Square the length of each leg (side a and side b). This means you have to multiply each number by itself.

For example:

If side a = 3 and side b = 4,

Square of side a = a^2 = 3 * 3 = 9

Square of side b = b^2 = 4 * 4 = 16

Step 4: Add Squares Together

Add together both squared values from Step 3 to find their sum.

Continuing with our example:

Sum of squared sides = a^2 + b^2 = 9 + 16 = 25

Step 5: Calculate Square Root

Find the square root of the sum calculated in Step 4. The result will be the length of the hypotenuse (side c).

In our example:

Square root of 25 = √25 = 5

So, the hypotenuse of the right triangle in our example is 5 units long.

Conclusion:

Calculating the hypotenuse of a right triangle is as simple as applying the Pythagorean theorem, which helps you find the length of the longest side. By following these five easy steps, you can quickly determine the hypotenuse length for any right-angled triangle.