If an angle in standard position has its terminal side passing through the point $(2,5)$ in the coordinate plane, what is the measure of the angle (in degrees) to the nearest tenth? $42.5°$ $67.5°$ $85°$ $135°$

• A. $85°$
• B. $42.5°$
• C. $68.2°$
• D. $135°$

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 given as \((2, 5)\).
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 \( \frac{y}{x} = \frac{5}{2} \). This ratio represents \( \tan(\theta) \).
4. Use the inverse tangent function (arctangent) to find the angle \( \theta \) in radians or degrees: \( \theta = \tan^{-1}\left(\frac{5}{2}\right) \).
5. Convert the angle to degrees if necessary and round to the nearest tenth to get the measure of the angle in degrees.