Final answer:
To find b in a right triangle given a and c, we use the Pythagorean theorem equation a² + b² = c² and solve for b.
Step-by-step explanation:
We can solve for the missing side using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. The equation is given by a² + b² = c². Rearranging the equation to solve for b, we have b = √(c² - a²).
Substituting the given values, we have b = √(9² - 5²) = √(81 - 25) = √56 = 2√14. Therefore, the value of b is 2√14.