Geometry

Question Analysis

This question focuses on applying trigonometric functions, specifically the tangent 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 tangent of ∠Q.

 

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 opposite  is , and the side adjacent to  is .

Using the formula , we get

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