Geometry

Question Analysis

The main focus of this problem is to use inverse trigonometric functions to find the unknown angle in a right - triangle. We need to determine the correct trigonometric ratio based on the given side lengths relative to angle and then set up the appropriate inverse trigonometric equation.

 

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 of length is opposite to angle , and the side of length is adjacent to angle .

2. Recall the tangent function definition:

Since , substituting the values, we get

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