Answer:
9.4 miles
Step-by-step explanation:
If Carlos walked 10 miles at an angle of [tex]20\degree[/tex] north of due east, then how far he moved east, which is [tex]x[/tex] can be calculated using trigonometry.
The side opposite to the known angle is [tex]x[/tex] miles.
The hypotenuse of the right triangle formed is [tex]10[/tex] miles.
We use the cosine ratio to obtain;
[tex]\cos(20\degree)=\frac{x}{10}[/tex]
[tex]\Rightarrow x=10\cos(20\degree)[/tex]
[tex]\Rightarrow x=9.396926208[/tex]
[tex]\therefore x=9.4[/tex] miles to the nearest tenth.
