Geometry

Question Analysis

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

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. First, note that and are similar. In right - triangle , , , .

2. For (which has the same cosine value as the corresponding angle in due to similarity), the side adjacent to (corresponding to the side adjacent in ) is (corresponding to ) and the hypotenuse is (corresponding to ).

3. Using the formula