Final answer:
The length of the hypotenuse of a 45-45-90 triangle with legs of 8 units is 8√2 units, calculated using the Pythagorean theorem.
Step-by-step explanation:
The question relates to solving for the hypotenuse of a right triangle using the Pythagorean theorem. For a 45-45-90 triangle with legs of equal length, the formula for the hypotenuse (c) becomes c = √(8² + 8²) since both legs (a and b) are 8 units. Using the Pythagorean theorem, we calculate the hypotenuse as follows:
- c = √(8² + 8²)
- c = √(64 + 64)
- c = √128
- c = √(64 * 2)
- c = √64 * √2
- c = 8√2
Therefore, the length of the hypotenuse is 8√2 units.