Geometry

Question Analysis

We are given two sides (, ) and an included angle () in , and we need to find the measure of using the Law of Cosines. First, we'll use the Law of Cosines to find the length of side , and then use the Law of Sines or the Law of Cosines again to find .

 

Key Concept Explanation

The Law of Cosines formula for finding a side is , where , are two sides of a triangle, is the included angle between them, and is the side opposite to angle . To find an angle, we can rearrange it as . The Law of Sines states that .

 

Step - by - Step Solution

1. Find the length of side :

Let , , .

Using the Law of Cosines .

, , and

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