An angle in standard position has its initial side along the positive $x$-axis. If its terminal side passes through the point $(4,15)$, what is the measure of the angle in degrees, rounded to the nearest whole number?

• A. $75°$
• B. $80°$
• C. $77°$
• D. $66°$

Answer: (A)

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 (4, 15).
2. Recall that the angle \( \theta \) in standard position can be found using the tangent function, since \( \tan(\theta) = \frac{y}{x} \), where \(x\) and \(y\) are the coordinates of the point.
3. Calculate the ratio \( \frac{y}{x} = \frac{15}{4} \) to find the value of \( \tan(\theta) \).
4. Use the inverse tangent function (arctangent) to find the angle \( \theta = \tan^{-1}\left(\frac{15}{4}\right) \). This will give the angle in radians or degrees depending on your calculator settings.
5. Make sure your calculator is set to degrees, then compute the inverse tangent value and round the result to the nearest whole number to find the measure of the angle in degrees.