If an angle $s$ in standard position has its terminal side passing through the point $(3,4)$ on the coordinate plane, what is the measure of angle $s$ to the nearest degree?

• A. $53°$
• B. $101°$
• C. $93°$
• D. $48°$

Answer: (A)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of angle \(s\) passes. Here, the point is \((3, 4)\).
2. Recall that the angle \(s\) in standard position is measured from the positive x-axis to the terminal side. To find \(s\), we can use the tangent function, which relates the y-coordinate and x-coordinate of the point: \(\tan(s) = \frac{y}{x}\).
3. Substitute the coordinates into the tangent formula: \(\tan(s) = \frac{4}{3}\).
4. To find the angle \(s\), take the inverse tangent (arctangent) of \(\frac{4}{3}\): \(s = \arctan\left(\frac{4}{3}\right)\).
5. Use a calculator to find the angle in degrees from the arctangent value, and round to the nearest degree to get the measure of angle \(s\).