How to Solve the Hypotenuse of a Triangle

The longest side is the hypotenuse.

The Pythagorean Theorem is one of the most well-known math formulas, giving us insight to the relationship between angles in a right triangle. Right triangles have one 90-degree angle and the hypotenuse is the longest side making up the triangle. When you're given the length of side "a" and side "b", you can figure out the length of "c" using the Pythagorean formula: a squared + b squared = c squared. From there, find the square root of c to get your answer.

Instructions

1. Find the value of "a" and "b," or the two shorter sides of the right triangle. When you're solving for the hypotenuse alone, these two values are given as numbers along the "a" and "b" lines.

2. Square the value of "a" and "b." For example, if "a" is 10 and "b" is 24, "a" squared is 100 and "b" squared is 576. When you square a number, you are multiplying that number by itself: 10 x 10 and 24 x 24.

3. Add the squared values of "a" and "b." In our example, 100 + 576 = 676.

4. Find the squared root of the total in Step 3. Use a calculator or divide the number you want to find the square root of by a number you think would square up to that number. For example, when finding the square root of 25, you might guess that four can square up to 25. Multiplying 4 x 4 shows us that the four squares up to 16. When we go up and try the number 5, we see that 5 x 5 squares up to 25, so 5 is the square root of 25. In the example above, the square root of 576 is 26 because 26 x 26 = 576. In this example, "c", or the hypotenuse, equals 26.

References

• Clark University: Right Triangles
• Math Warehouse: Right Triangles: Pythagorean Theorem
• Algebra Lab: Pythagorean Theorem

Resources

• Math: Square Root Calculator