Given that angle $DFE$ is in standard position and its terminal side passes through the point $\left(4,,,3\right)$, what is the measure of angle $DFE$ to the nearest degree?

• A. $64°$
• B. $58°$
• C. $32°$
• D. $29°$

Answer: (C)

Verified step by step guidance

1. Identify that the angle \( \angle DFE \) 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 \( (4, 3) \). This point gives the coordinates \( x = 4 \) and \( y = 3 \).
3. Use the tangent function to find the angle formed by the terminal side with the positive x-axis. Recall that \( \tan(\theta) = \frac{y}{x} \), so here \( \tan(\theta) = \frac{3}{4} \).
4. Calculate the angle \( \theta \) by taking the inverse tangent (arctangent) of \( \frac{3}{4} \), i.e., \( \theta = \arctan\left(\frac{3}{4}\right) \).
5. Convert the angle from radians to degrees if necessary, and round the result to the nearest degree to find the measure of \( \angle DFE \).