Geometry

Question Analysis

This question focuses on applying trigonometric functions, specifically the sine 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 sine of ∠R.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. First, consider right - triangle where , , , and .

Since and are similar (by AA similarity or other geometric relationships in the figure), the ratios of corresponding sides are the same.

In right - triangle , for (which is equal to due to similarity), the side opposite is , and the hypotenuse is .

2. Then, calculate

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