Geometry

Question Analysis

This question is about applying trigonometric functions, specifically the tangent function, in right - angled triangles. The key is using the side - length relationships to find the tangent of ∠R. Since the triangles are similar, we can use the side lengths of the known triangle  to solve.

 

Key Concept Explanation:

In a right - triangle, for an acute angle , the tangent is defined as .

 

Step-by-Step Solution

In right - triangle , . If  is corresponding to  (due to similarity), for :

The side opposite  is , and the side adjacent to  is .

Using the tangent formula , we get

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