Final answer:
To find the hypotenuse of a right triangle with leg lengths of 15 Sqrt2, use the Pythagorean theorem. The formula simplifies to a hypotenuse length of 30 units.
Step-by-step explanation:
The student is asking to find the length of the hypotenuse (HYP) of a right-angled triangle when the lengths of the legs are given as 15 Sqrt2. 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), we can find the hypotenuse.
The theorem is expressed as a² + b² = c². Substituting our given values, we get (15 Sqrt2)² + (15 Sqrt2)² = c², which simplifies to 450 + 450 = c², and further simplifies to 900 = c². Taking the square root of both sides, we find that c = 30. Thus, the length of the hypotenuse is 30 units.