Final answer:
A Pythagorean triplet is a set of three positive integers that satisfy the equation a^2 + b^2 = c^2. To find a Pythagorean triplet where one number is 8, we can substitute 8 for a and solve for b and c. The Pythagorean triplet where one number is 8 is (8, 6, 10).
Step-by-step explanation:
A Pythagorean triplet is a set of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2. To find a Pythagorean triplet where one number is 8, we can substitute 8 for a and solve for b and c.
Using the Pythagorean theorem, we have 8^2 + b^2 = c^2. Simplifying this equation gives us 64 + b^2 = c^2. By finding the square roots of both sides, we get b = sqrt(c^2 - 64).
Now, we can choose a value for c and solve for b. For example, let's take c = 10. Substituting this value into the equation gives us b = sqrt(10^2 - 64) = sqrt(36) = 6. Therefore, the Pythagorean triplet where one number is 8 is (8, 6, 10).