In △XYZ, XY = 17, YZ = 23, ZX = 31. The measure of ∠Y is ________°. (Round to the nearest tenth.)
Answer & Analysis
Analysis
Question Analysis
The task is to find the measure of in using the Law of Cosines, given all three side lengths (, , ).
Key Concept Explanation
The Law of Cosines formula for an angle is , where is the angle between sides and , and is the side opposite . For , the sides adjacent are and , and the opposite side is . Thus, .
Step-by-Step Solution
1. Identify values: Let , , .
2. Calculate:
Squares:
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