11. Using the Pythagorean theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long. A. \( \sqrt{41 \mathrm{ft}} \) B. 12.81 ft C. 6 ft . D. 36 ft .

To find the length of the unknown leg \( b \) of a right triangle using the Pythagorean theorem, we can use the formula \( a^2 + b^2 = c^2 \), where \( a \) is the length of one leg, \( b \) is the length of the other leg, and \( c \) is the hypotenuse. Here, we have \( a = 8 \) feet and \( c = 10 \) feet. Rearranging the formula gives us \( b^2 = c^2 - a^2 \). Plugging in the values: \( b^2 = 10^2 - 8^2 = 100 - 64 = 36 \). Thus, \( b = \sqrt{36} = 6 \) feet. So the answer is C. 6 ft. Did you know that the Pythagorean theorem, discovered by the ancient Greek mathematician Pythagoras, has been around for over 2,500 years? It’s not just a vital tool for geometry, but also a fundamental concept in architecture, navigation, and even computer science! This theorem helps us calculate distances and check for right angles, making it an essential element in both theory and practice. Now, if you ever find yourself stuck on a problem involving right triangles, remember to double-check your calculations! A common mistake is forgetting to square your numbers correctly or mixing up the sides. Always make sure \( c \) (the hypotenuse) is the longest side, and you'll be on the right track!