A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?
Accepted Solution
A:
Answer:[tex]174.66\ mi[/tex] or [tex]175\ mi[/tex]Step-by-step explanation:we know thatApplying the law of cosines[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]In this problem we have[tex]a=200\ mi[/tex][tex]b=30\ mi[/tex][tex]C=30\°[/tex]substitute the values[tex]c^{2}=200^{2}+30^{2}-2(200)(30)cos(30\°)[/tex][tex]c^{2}=30,507.695[/tex][tex]c=174.66\ mi[/tex]