Answer:
To solve the Pythagorean theorem, which relates the lengths of the sides of a right triangle, follow these steps:
1. Identify the right triangle: Ensure that the triangle you are working with has one angle measuring 90 degrees (a right angle). This is necessary for the Pythagorean theorem to apply.
2. Label the sides: Assign labels to the three sides of the right triangle. The two shorter sides are typically labeled as "a" and "b," while the longest side (the hypotenuse) is labeled as "c."
3. Understand the theorem: The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Mathematically, this can be expressed as c^2 = a^2 + b^2.
4. Solve for the missing side: If you know the lengths of two sides, you can find the length of the third side using the Pythagorean theorem. To find the length of the missing side:
a. Square the lengths of the known sides.
b. Add the squares together.
c. Take the square root of the sum to find the length of the missing side.
5. Use units: Don't forget to include units in your final answer, such as inches or centimeters, depending on the context of the problem.
For example, let's say you have a right triangle with side lengths of 3 units for side "a" and 4 units for side "b." To find the length of the hypotenuse (side "c"), you would follow these steps:
a. Square the lengths of the known sides: 3^2 = 9 and 4^2 = 16.
b. Add the squares together: 9 + 16 = 25.
c. Take the square root of the sum: √25 = 5.
d. Therefore, the length of the hypotenuse (c) is 5 units.