The hypotenuse of a right triangle measures 15 cm and one of its legs measures 6 cm . Find the measure of the other leg. If necessary, round to the nearest tenth.

To find the measure of the other leg of the right triangle, you can use the Pythagorean theorem, which states that \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, the hypotenuse \(c = 15\) cm and one leg \(a = 6\) cm. You can calculate the other leg \(b\) as follows: 1. Plug the values into the formula: \(6^2 + b^2 = 15^2\) \(36 + b^2 = 225\) 2. Subtract \(36\) from both sides: \(b^2 = 225 - 36\) \(b^2 = 189\) 3. Now take the square root: \(b = \sqrt{189} \approx 13.8\) cm. So, the measure of the other leg is approximately 13.8 cm! Now that you've got that figured out, it's worth noting that the Pythagorean theorem isn't just a classroom concept; it has practical applications in fields like architecture, engineering, and even game development. When building structures, architects need to ensure that angles and lengths align correctly, and the theorem helps them calculate distances accurately. Also, while working with right triangles, it's easy to confuse the legs with the hypotenuse. Remember, the hypotenuse is always opposite the right angle and is the longest side, which can lead to errors in calculation. So, always double-check whether you're using the correct sides when applying the theorem!