Geometry

Question Analysis

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

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Find the short leg :

Since the side with length  is the hypotenuse (opposite 90°), and the formula for the hypotenuse is . Let the short leg be .

Set , then .

2. Find the long leg

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