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

• A. $67°$
• B. $90°$
• C. $53°$
• D. $37°$

Answer: (C)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is (3, 4).
2. Recall that the angle in standard position has its vertex at the origin (0,0) and its initial side along the positive x-axis. The terminal side passes through (3, 4).
3. Use the tangent function to find the angle measure, since \( \tan(\theta) = \frac{y}{x} \) for a point (x, y) on the terminal side. Substitute the values: \( \tan(\theta) = \frac{4}{3} \).
4. Calculate the angle \( \theta \) by taking the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
5. Convert the angle from radians to degrees if necessary, and then approximate the value to find the best matching angle measure from the given options.