Geometry

Question Analysis

This question focuses on applying the tangent function in the context of similar right - angled triangles. The key is to use the side - length ratios of the smaller right - triangle  to find the tangent of ∠M, leveraging the similarity relationship between triangles.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. In right - triangle , ∠OPN = 90°. The side opposite ∠PON is , and the side adjacent to ∠PON is .

2. Calculate tan∠PON using the formula: