Geometry

Question Analysis

This question focuses on applying trigonometric functions, specifically the cosine function, in the context of similar right - angled triangles. The key is to use the side - length ratios of the given right - triangle to find the cosine of ∠M.

 

Key Concept Explanation:

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

 

Step-by-Step Solution

In right - triangle with , if is corresponding to (due to similarity):

The side adjacent to is , and the hypotenuse is .

Using the formula , we get

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