Given that angle $yzx$ is in standard position and its terminal side passes through the point $(3,4)$, which is the approximate measure of angle $yzx$ in degrees?

• A. $120°$
• B. $37°$
• C. $67°$
• D. $53°$

Answer: (D)

Verified step by step guidance

1. Identify that the angle \( yzx \) is in standard position, meaning its vertex is at the origin and its initial side lies along the positive x-axis.
2. Recognize that the terminal side of the angle passes through the point \( (3, 4) \). This point can be used to find the angle's measure by considering the right triangle formed with the x-axis.
3. Calculate the tangent of the angle using the coordinates of the point: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{4}{3} \).
4. Use the inverse tangent function to find the angle in degrees: \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
5. Interpret the result from the inverse tangent calculation as the approximate measure of angle \( yzx \) in degrees.