Geometry

Question Analysis

The main focus of this question is to find the tangent of  in a right - triangle. It requires understanding the definition of tangent and correctly identifying the opposite and adjacent sides relative to .

 

Key Concept Explanation

In a right - triangle, the tangent of an acute angle  is defined as . The opposite side is the side directly opposite the angle , and the adjacent side is the side next to  (excluding the hypotenuse).

 

Step - by - Step Solution

1. Find the length of side :

Using the Pythagorean theorem , where  (hypotenuse) and . Let , then .

2. Identify the sides relative to :

The side opposite to  is , and the side adjacent to