Question

TRIGONOMETRY (adding vectors algebraically)Find the direction of the cars resultant vector

Answer 1

$\theta=50.9^{\circ}$

1) Let's sketch out this to better understand it:

Note that there are two vectors here, as we were told and a third one the resultant. So let's find the direction of this blue and resultant vector:

2) Now, let's calculate the tangent of that angle theta, and then the arctangent to find the angle that gives us the direction of that resultant.

$\begin{gathered} \tan (\theta)=\frac{16}{13} \\ \theta=\tan ^{-1}(\frac{16}{13}) \\ \theta=50.9^{\circ} \end{gathered}$

Thus, this is the direction of the car's resultant vector 50.9º