Geometry

Question Analysis

This question focuses on applying the properties of 30 - 60 - 90 right - triangles to find the lengths of the missing sides. The key is to use the established side - length relationships in such triangles.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Identify the short leg:

The side with length  is opposite the 30° angle, so it is the short leg. Let .

2. Find the length of the long leg :

The long leg  is opposite the 60° angle. Using the formula , substitute . Then