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

 

Step - by - Step Solution

1. Identify the sides relative to angle :

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

2. Apply the cosine function:

Since

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