Final answer:
To determine the length of the hypotenuse of a right triangle with legs 40 and 75, use the Pythagorean theorem, which yields a hypotenuse length of 85 units.
Step-by-step explanation:
To find the length of the hypotenuse in a right triangle using the Pythagorean theorem, one must square the lengths of both legs of the triangle, sum these squares, and then take the square root of this sum. In this case, the triangle's sides are 40 and 75. According to the theorem, we calculate the hypotenuse c as follows:
c = √(40² + 75²)
This simplifies to:
c = √(1600 + 5625)
c = √7225
Hence, the length of the hypotenuse c is √7225, which equals 85. The hypotenuse is 85 units long.