In a 45-45-90 triangle, the legs are each $$\frac{\sqrt{2}}{...

Question Analysis

Determine the hypotenuse of a 45-45-90 triangle with legs of length , using the triangle’s side ratio properties.

Key Concept Explanation

45-45-90 Triangle Ratio: Legs are equal (), and hypotenuse .

For legs scaled to the unit circle (), the hypotenuse remains 1 (since it’s the unit circle radius).

Step-by-Step Solution

1. Apply the hypotenuse formula:

2. Simplify:

Option Analysis

1: Correct (matches unit circle hypotenuse)

: Incorrect (too small; hypotenuse must be longer than legs)

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Geometry