Geometry

Question Analysis

The main focus is using trigonometric functions in right - triangle (where ) to find the length of side . Given and the length of the hypotenuse , we need to determine the length of the side opposite to .

 

Key Concept Explanation

In a right - triangle, the sine of an angle is defined as . Here, , the hypotenuse is , and the opposite side is .

 

Step - by - Step Solution

1. Identify the relevant trigonometric function:

Since we know the hypotenuse and want to find the side opposite to the given angle, we use the sine function. The formula is .

2. Substitute the known values:

Given and