Given a point $(3,4)$ on the terminal side of an angle $\angle$ in standard position, what is the measure of angle $ACB$ in degrees?

• A. $60°$
• B. $36.87°$
• C. $53.13°$
• D. $45°$

Answer: (C)

Verified step by step guidance

1. Identify the coordinates of the point on the terminal side of the angle: here, the point is (3, 4).
2. Recall that the angle in standard position is formed by the positive x-axis and the line segment from the origin to the point (3, 4).
3. Use the tangent function, which relates the angle \( \theta \) to the ratio of the y-coordinate to the x-coordinate: \( \tan(\theta) = \frac{y}{x} \). Substitute the values: \( \tan(\theta) = \frac{4}{3} \).
4. To find the angle \( \theta \), take the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
5. Use a calculator set to degree mode to evaluate \( \tan^{-1}\left(\frac{4}{3}\right) \), which will give the measure of the angle in degrees.