How Do You Find the Hypotenuse of an Isosceles Triangle, Given Two Lengths?

Use the Pythagorean theorem to calculate the hypotenuse of a right triangle. A right triangle is a type of isosceles triangle. The hypotenuse is the side of the triangle opposite the right angle.

  1. Make certain the triangle is a right triangle

    The Pythagorean theorem can only be used with isosceles triangles that are right triangles. This means one of the angles must be 90 degrees. If it’s not, the theorem cannot be used.

  2. Write down the Pythagorean theorem

    The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the two shorter legs. It’s often written as h squared equals a squared plus b squared.

  3. Insert the numbers

    Replace a and b in the equation with the lengths of the two sides. As an example, let a = 3 and b = 4.

  4. Square both of the lengths

    To find the square of a number, multiply it by itself. For example, to find the square of 3, multiply 3 by 3 to get 9. For 4, multiply 4 by 4 to get 16.

  5. Add the two squares

    Add the results of the two calculations. In the example, 9 + 16 = 25. The equation now reads h squared = 25.

  6. Calculate the hypotenuse by figuring the square root of the result

    To remove the squared part of the equation, take the square root of both sides. The square root of h squared is simply h, the length of the hypotenuse. To find the square root of a number, determine what number multiplied by itself is equal to that number. In the example, the square root of 25 is 5 because 5 * 5 = 25. In many cases, the square root is not a whole number.