Geometry

Question Analysis  

The question asks for the hypotenuse length in a unit circle triangle for any angle , focusing on the definition of the unit circle.  

 

Key Concept Explanation  

Unit Circle Definition: The unit circle has a radius of 1. For any angle , the hypotenuse of the right triangle formed (with legs as and ) is equal to the radius, which is 1.  

 

Step-by-Step Solution  

1. Recall the unit circle radius: By definition, the radius .  

2. Hypotenuse in trigonometry: In the unit circle, the hypotenuse of the triangle corresponding to angle is the radius itself.  

3. Conclusion: Hypotenuse length = .  

 

Common Mistakes  

Confusing hypotenuse with leg lengths (e.g.,

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