Geometry

Question Analysis

This question focuses on using the properties of 30 - 60 - 90 right - triangles to find the lengths of the unknown sides. The key is applying the side - length relationships specific to these 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:

Since the side with length 10 is opposite the 60° angle, it is the long leg. Let the short leg (opposite 30° angle) be .

Using the formula for the long leg , and given the long leg is 10, we have . Solving for , we divide both sides by , getting , so .

2. Find the length of the hypotenuse

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