Given that angle $\angle DAE$ is in standard position and its terminal side passes through the point $(3,4)$, what is the measure of $\angle DAE$ in degrees?

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

Answer: (D)

Verified step by step guidance

1. Identify that the angle \( \angle DAE \) is in standard position, meaning its vertex is at the origin and its initial side lies along the positive x-axis.
2. Recognize that the terminal side of the angle passes through the point \( (3, 4) \), which gives the coordinates \( x = 3 \) and \( y = 4 \).
3. Use the definition of the tangent function in a right triangle formed by the point and the origin: \( \tan(\theta) = \frac{y}{x} \). Substitute the values to get \( \tan(\theta) = \frac{4}{3} \).
4. Find the angle \( \theta \) by taking the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
5. Convert the angle from radians to degrees if necessary, and interpret the result as the measure of \( \angle DAE \) in degrees.