A vector in the xy plane has a magnitude of 25 and an x component of 12.The angle it makes with the positive x axis is:
A)26 $\degree$
B)29 $\degree$
C)61 $\degree$
D)64 $\degree$
E)241 $\degree$

Question

Quizplus · Accepted Answer

We can use the formula $	heta = 	an^{-1}(\frac{y}{x})$ to find the angle that the vector makes with the positive x-axis, where $y$ is the y-component of the vector. Since the vector lies in the xy plane, its y-component is $\pm \sqrt{25^2-12^2}=\pm 19$. Since the x-component is positive and the y-component is positive, we take the positive value for the y-component. Thus, the angle with the positive x-axis is $	heta = 	an^{-1}(\frac{19}{12}) \approx \boxed{	extbf{(C)}\ 61^\circ}$.

A Vector in the Xy Plane Has a Magnitude of 25