Geometry

Question Analysis:
This question combines the properties of equilateral and right - triangles.
The main focus is to use the properties of an equilateral triangle to find the length of one side, and then use the angle - side relationship in the right - triangle to determine the length of .

Key Concept Explanation:
- Equilateral Triangle Properties: In an equilateral triangle, all three angles are equal, each measuring , and all three sides are of equal length.
- Isosceles Triangle Determination: In a triangle, if two angles are equal, then the sides opposite those angles are equal, making it an isosceles triangle.

Step - by - Step Solution:
1. Since is an equilateral triangle, by the property that all sides of an equilateral triangle are equal, and given , we have .
2. Because in , by the property that in a triangle, equal angles have equal opposite sides, we can conclude that

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