Geometry

Question Analysis

This question focuses on applying trigonometric functions, specifically the cosine function, in the context of right - angled triangles. The main task is to use the side - length ratios to find the cosine of ∠G.

 

Key Concept Explanation

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

 

Step - by - Step Solution

In right - triangle  (which is part of the figure and can be used to analyze the similar - triangle relationships for ), .

For ∠MNE (and since  is corresponding to ∠MNE due to similarity), the side adjacent to ∠MNE is , and the hypotenuse is .

Using the formula , we get 

Option Analysis

A.: Incorrect. This ratio does not match the cosine definition for  as 15 is not the hypotenuse relative to .

B.

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