Final answer:
To find b and c in the Pythagorean triple with a = 5, substitute the given values into the equation 5² + b² = c². Guess values for b and calculate the corresponding value of c using the equation. There are multiple possible values for b and c that satisfy the equation.
Step-by-step explanation:
The Pythagorean theorem relates the lengths of the legs of a right triangle, labeled a and b, with the length of the hypotenuse, labeled c. The relationship is given by the formula a² + b² = c².
In this case, we are given a = 5. To find b and c, we can substitute the given values into the equation: 5² + b² = c².
Simplifying this equation gives us 25 + b² = c². Since we are looking for Pythagorean triples, we can start by guessing values for b and calculating the corresponding value of c using the equation. Here are a few examples:
- If b = 12, then 25 + 12² = c², which simplifies to 25 + 144 = c². This gives us c = √169 = 13.
- If b = 24, then 25 + 24² = c², which simplifies to 25 + 576 = c². This gives us c = √601 = 24.53 (rounded to two decimal places)
- If b = 8, then 25 + 8² = c², which simplifies to 25 + 64 = c². This gives us c = √89 = 9.43 (rounded to two decimal places)
These are just a few examples, and there are many more possible values for b and c that satisfy the equation. The Pythagorean theorem allows us to find the relationship between the sides of a right triangle.