Geometry

Question Analysis

This problem requires using inverse trigonometric functions to find the measure of angle in a right - triangle. The key is to determine the correct trigonometric ratio based on the side lengths relative to angle and then apply the corresponding inverse function.

 

Key Concept Explanation

For an acute angle in a right - triangle:

.

The inverse cosine function, , is used to find the angle when the cosine ratio 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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