Geometry

Question Analysis

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

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Identify the sides relative to :

First, find the length of the hypotenuse  using the Pythagorean theorem , where , . So, .

The side adjacent to  is .

The hypotenuse is .

2. Calculate :

Using the formula