Geometry

Question Analysis

This question focuses on using inverse trigonometric functions to find the measure of angle in a right - triangle. We need to identify the appropriate trigonometric ratio based on the 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 tangent function is used to find the angle when the tangent ratio of the sides is known. That is, if , then .

 

Step - by - Step Solution

1. Identify the sides relative to angle :

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

2. Apply the tangent function:

Since

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