Geometry

Question Analysis

The main focus of this problem is to use inverse trigonometric functions to find the measure of angle  in a right - triangle. We need to identify the appropriate trigonometric ratio based on the given side lengths relative to angle  and then use the inverse trigonometric function to calculate the angle.

 

Key Concept Explanation

In a right - triangle, for an acute angle :

.

The inverse tangent function  is used to find the angle when the tangent ratio of the sides is known. That is, if , then .

 

Step - by - Step Solution

1. Identify the sides relative to angle :

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

2. Apply the tangent function:

Since