Geometry

Question Analysis

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

 

Key Concept Explanation

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

 

Step - by - Step Solution

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

2. Then, apply the Law of Sines. Let ,

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