Geometry

Question Analysis

The main focus is using the properties of 30 - 60 - 90 triangles to find the lengths of sides  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 opposite the 60° angle (long leg), and the formula for the long leg is . Let the short leg be .

We have , dividing both sides by , we get