Given that angle $xyz$ is in standard position and its terminal side passes through the point $(40,28)$, which is the best approximation for the measure of angle $xyz$ in degrees?

• A. $56.4°$
• B. $33.6°$
• C. $39.8°$
• D. $50.2°$

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 (40, 28).
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 the point (40, 28).
3. To find the measure of the angle \( \angle xyz \), calculate the angle \( \theta \) that the terminal side makes with the positive x-axis. Use the tangent function, which relates the y-coordinate and x-coordinate of the point: \[ \tan(\theta) = \frac{y}{x} = \frac{28}{40} \].
4. Find the angle \( \theta \) by taking the inverse tangent (arctangent) of the ratio: \[ \theta = \tan^{-1} \left( \frac{28}{40} \right) \]. This will give the angle in radians or degrees depending on your calculator settings.
5. Make sure your calculator is set to degrees mode, then compute the inverse tangent to get the angle measure in degrees, which approximates the measure of \( \angle xyz \).