Question

You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?

Answer 1

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

$\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}$

so, we need a function that relates those values

$\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}$

replace

$\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}$

so, the direction is

N 60° W