Geometry

Question Analysis

This question focuses on applying the cosine function in the context of similar right - angled triangles. The key is to correctly identify the adjacent side and hypotenuse relative to ∠Z and use the cosine formula.

 

Key Concept Explanation

In a right - triangle, for an acute angle , .

 

Step - by - Step Solution

1. First, since .

In right - triangle , , , and .

For ∠Z, the side adjacent to ∠Z in is . The hypotenuse is .

Because of the similarity of the triangles, the ratio of the sides in can be used to find the ratio for ∠Z. The side corresponding to in is , and the side corresponding to is .

2. Then, using the cosine formula

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