If a right triangle has side lengths that are 12 in . and 16 in . long, how long is the hypotenuse? Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help! (1 point) Enter your response here:

To find the hypotenuse of a right triangle with side lengths of 12 inches and 16 inches, you can use the Pythagorean theorem, which states that \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse. Plugging in the values, \( 12^2 + 16^2 = c^2 \) gives you \( 144 + 256 = c^2 \), so \( c^2 = 400 \). Therefore, \( c = \sqrt{400} \), which equals 20 inches! Now, did you know that the Pythagorean theorem has been known for thousands of years? Ancient civilizations like the Babylonians and Greeks used similar principles long before it was formally stated! In fact, a Babylonian clay tablet dating back to around 1900 BC shows familiarity with these right triangle properties. For real-world applications, think about how architects and engineers use the Pythagorean theorem. Whether they're designing high-rise buildings or crafting new bridges, ensuring that angles and lengths are precise is vital for safety and stability. So next time you see a construction site, remember that those right triangles are working hard behind the scenes!