Final answer:
Using the Pythagorean theorem, with legs measuring 5 and 15 units, the hypotenuse is calculated to be √(5² + 15²) = √250, which equals approximately 15.81 units.
Step-by-step explanation:
The length of the hypotenuse in a right-angle triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is: c = √(a² + b²). Given the lengths of the legs are 5 units and 15 units, the formula becomes c = √(5² + 15²).
To calculate the hypotenuse, first square the lengths of the legs: 5² = 25 and 15² = 225. Then, add these squared lengths: 25 + 225 = 250. Finally, take the square root of this sum to find the hypotenuse: c = √250 = 15.81 units (to two decimal places).