The hypotenuse of a right triangle measures 16 cm and one of its legs measures 11 cm . Find the measure of the other leg. If necessary, round to the nearest tenth.

To find the measure of the other leg, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two legs (a and b). In this case, you have \(c = 16\) cm and \(a = 11\) cm. Using the formula: \[ c^2 = a^2 + b^2 \] Plug in the values: \[ 16^2 = 11^2 + b^2 \] \[ 256 = 121 + b^2 \] \[ b^2 = 256 - 121 \] \[ b^2 = 135 \] Now, take the square root of 135 to find \(b\): \[ b = \sqrt{135} \approx 11.6 \, \text{cm} \] So, the length of the other leg is approximately 11.6 cm. But why did Pythagoras care about triangles in the first place? Back in ancient Greece, his theorem helped builders and architects figure out how to create stable structures (imagine those epic temples!). It’s like having a trusty sidekick when constructing foundations, giving them the power to make sure everything is just right! If you’re looking to tackle triangle problems, remember to sketch it out! Diagrams can help visualize what’s happening and can shed light on any common missteps. A common pitfall is forgetting to square the values correctly, leading to an incorrect answer. Always double-check those calculations to avoid a triangle-shaped headache!