Question

question 1 of 25
a vector has an x - component of length 3.5 and a y - component of length 3. what is the angle of the vector? (hint: use the inverse tangent.)
a. 31.0°
b. 59.0°
c. 40.6°
d. 67.2°

Explanation:

Step1: Recall tangent - angle formula

The tangent of the angle $\theta$ of a vector with $x$ - component $x$ and $y$ - component $y$ is given by $\tan\theta=\frac{y}{x}$.

Step2: Substitute given values

Here, $x = 3.5$ and $y = 3$. So, $\tan\theta=\frac{3}{3.5}=\frac{6}{7}$.

Step3: Calculate the angle

$\theta=\arctan(\frac{6}{7})$. Using a calculator, $\theta=\arctan(\frac{6}{7})\approx40.6^{\circ}$.

Answer:

C. $40.6^{\circ}$