How to Find the Base of a Right Triangle

By Jon Zamboni; Updated April 24, 2017
The Pythagorean theorem applies to right triangles only.

A right triangle is a triangle that has a right angle as one of its three angles. A right angle, or 90-degree angle, is the same type of angle found at one of a square's corners. A right triangle's base is one of its two legs, the two sides that meet in a right angle. You can use the Pythagorean theorem -- which shows the relationship between a right triangle's sides -- to find the length of the base.

The Pythagorean Theorem

The Pythagorean theorem is a formula that gives the relationship between the lengths of a right triangle's three sides. The triangle's two legs, the base and height, intersect in the triangle's right angle. The hypotenuse is the side of the triangle opposite the right angle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides:

a^2 + b^2 = c^2

In this formula, a and b are the lengths of the two legs and c is the length of the hypotenuse. The ^2 signifies that a, b, and c are squared. A number squared is equal to that number multiplied by itself -- for example, 4^2 is equal to 4 times 4, or 16.

Finding the Base

Using the Pythagorean theorem, you can find the base, b, of a right triangle if you know the lengths of the height, h, and the hypotenuse. Since the hypotenuse squared is equal to the height squared plus the base squared, then:

b^2 = c^2 - h^2

For a triangle with a hypotenuse of 5 inches and a height of 3 inches, find the base squared:

b^2 = (5 x 5) - (3 x 3) = 25 - 9 = 16

Since b^2 equals 16, then b equals the number that, when squared, makes 16. When you multiply 4 by 4, you get 16, so the square root of 16 is 4. The triangle has a base that is 4 inches long.

About the Author

Jon Zamboni began writing professionally in 2010. He has previously written for The Spiritual Herald, an urban health care and religious issues newspaper based in New York City, and online music magazine eBurban. Zamboni has a Bachelor of Arts in religious studies from Wesleyan University.