Geometry

Question Analysis

We are given two angles (, ) and one side () in . The goal is to find side . The Law of Sines will be our primary tool to establish the relationship between the known and unknown elements of the triangle.

 

Key Concept Explanation

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides. That is, for , .

 

Step - by - Step Solution

1. First, find . Since the sum of the interior angles of a triangle is , we have .

2. Then, apply the Law of Sines. Let , . According to the Law of Sines formula