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 hypotenuse:
The side with length 22 is opposite the 90° angle, so it is the hypotenuse. Let the short leg (opposite 30° angle) be . Since the hypotenuse , and the hypotenuse is 22, then , solving for gives . So the side .
2. Find the length of the long leg :
The long leg