Final answer:
Using the Pythagorean theorem (a² + b² = c²), the length of the other leg of a right triangle with a hypotenuse of 25 feet and a leg of 7 feet is found to be 24 feet by calculating the square root of the difference between the square of the hypotenuse and the square of the given leg.
Step-by-step explanation:
To find the length of the other leg of a right triangle when given one leg and the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is a² + b² = c².
Here, we have a leg of 7 feet (let's call this a) and a hypotenuse of 25 feet. We are solving for the other leg (b), so we rearrange the theorem to solve for b²: b² = c² - a².
Substituting the known values, we have: b² = 25² - 7² = 625 - 49 = 576. Taking the square root of both sides, we find that b = √576 = 24 feet.
Therefore, the length of the other leg is 24 feet.