Geometry

Question Analysis

We need to find side  in  with two angles (, ) and side  given. The Law of Sines is the essential tool to build the connection for solving the unknown side.

 

Key Concept Explanation

Law of Sines: In , . It means that the ratio of the length of each side to the sine of its opposite angle remains equal throughout the triangle, allowing us to find an unknown side when some angles and side lengths are known.

 

Step - by - Step Solution

1. Find :

As the sum of angles in a triangle is , .

2. Apply the Law of Sines:

Let , . According to the Law of Sines,