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 correct 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

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

, , .

The inverse trigonometric functions , ,  are used to find the angle when the ratio of the sides is known. For example, if , then ; if , then ; if , then .

 

Step - by - Step Solution

1. Identify the sides relative to angle :

The side opposite to angle  is