N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
[tex]\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}[/tex]
so, we need a function that relates those values
[tex]\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]
replace
[tex]\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}[/tex]
so, the direction is
N 60° W
