Question

A vector has an x-component of length 12 and a y-component of length 14.
What is the angle of the vector? (Hint: Use the inverse tangent.)

Answer 1

Answer:

∴ The angle of the vector is 49.4°.

Explanation:

Given:

For a vector:

$x-component\rightarrow 12$

$y-component\rightarrow 14$

The tangent of angle of a vector is given by:

$\tan \theta=\frac{y}{x}$

where $\theta$ represents the angle of the vector, $y$ represents the length of $y-component$ and $x$ represents the length of $x-component$.

Plugging in the given values to get the angle of vector $\theta$.

$\tan \theta=\frac{14}{12}$

Taking $\tan^{-1}$ both sides to get $\theta$

$\theta=\tan^{-1}\frac{14}{12}$

$\theta=49.4\°$

∴ The angle of the vector is 49.4°.