Geometry

Question Analysis

The main focus is identifying the long leg in a 30 - 60 - 90 triangle by understanding the side - angle relationships.

 

Key Concept Explanation

In a 30 - 60 - 90 triangle, the side opposite the 30° angle is the short leg, the side opposite the 60° angle is the long leg (with a length  times that of the short leg), and the side opposite the 90° angle is the hypotenuse (twice the length of the short leg).

 

Step - by - Step Solution

Since  is opposite the 30° angle,  is the short leg. The hypotenuse is  (opposite the 90° angle). So, the side opposite the 60° angle, which is

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