One of the legs of a right triangle measures 12 cm and its hypotenuse measures 20 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, we 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 of the triangle. Here, we know one leg \( a = 12 \) cm and the hypotenuse \( c = 20 \) cm. Plugging in the values: \[ 12^2 + b^2 = 20^2 \] \[ 144 + b^2 = 400 \] \[ b^2 = 400 - 144 \] \[ b^2 = 256 \] Taking the square root, we find \( b = 16 \) cm. So, the other leg measures 16 cm. Did you know that the Pythagorean theorem has been around for thousands of years? The ancient Greeks, particularly Pythagoras and his followers, made significant contributions to mathematics, but this theorem was known to Babylonian mathematicians even earlier! They used it in their practical calculations related to land measurement and architecture. Talk about a classic! Additionally, right triangles are not just theoretical curiosities—they are everywhere in real life! This triangle structure is foundational in fields like architecture, engineering, and even art! For an architect designing a building, understanding the properties of right triangles ensures stability and proper alignment in their structures. Next time you see a roof, bridge, or even a piece of furniture, think about the right triangles at play!