The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The document provides examples of using the Pythagorean theorem to solve for the unknown hypotenuse or leg of a right triangle by substituting values into the formula a2 + b2 = c2, where c is the hypotenuse and a and b are the legs. It also describes how to find the angles of a right triangle using relationships between sides and angles.
2. The Formula
The picture below shows the formula for the Pythagorean theorem. In
the pictures below, side C is always the hypotenuse. Remember that
this formula only applies to right triangles.
3. Examples of the Pythagorean Theorem
When you use the Pythagorean theorem, just remember that the
hypotenuse is always 'C' in the formula above . Look at the following
examples to see pictures of the formula.
4. Step 1) Identify the legs and the
Example 1 (solving hypotenuse of the right triangle.
for the hypotenuse) The legs have length '6 and '8' . 'X' is
the hypotenuse because it is opposite
Use the Pythagorean theorem to the right angle.
determine the length of X
Step 2) Substitute values into the
formula (remember 'c' is the
hypotenuse)
A2 + B2 = C2
62 + 82 = X2
Step 3) Solve for the unknown
5. Example 2 (solving for
Step 1) Identify the legs and the
a Leg) hypotenuse of the right triangle
The legs have length '24' and 'X'
Use the Pythagorean theorem to are the legs. The hypotenuse is 26.
determine the length of X
Step 2) Substitute values into
the formula (remember 'c' is the
hypotenuse)
A2 + B2 = C2
x2 + 242 = 262
Step 3) Solve for the unknown