Geometry

Question Analysis

This question focuses on using inverse trigonometric functions to find the measure of angle in a right - triangle. We can directly use the cosine function based on the given side lengths relative to angle and then apply the inverse cosine 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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