Geometry

Question Analysis

The main focus is applying the side - length relationships of 30 - 60 - 90 right - triangles to find the lengths of sides  and .

 

Key Concept Explanation

In a 30 - 60 - 90 right - triangle, if the short leg (opposite 30°) is , the long leg (opposite 60°) is , and the hypotenuse (opposite 90°) is .

 

Step - by - Step Solution

1. Find the short leg :

Since the hypotenuse is  and hypotenuse = 2x, we solve for  (the short leg ):

Set , then .

2. Find the long leg