Question

An ant travels 2.78 cm (West) and then turns and travels 6.25 cm (South 40 degrees East). What is the ant's total displacement?

Answer 1

$From\ cosine\ theorem:\\\\ c^2=a^2+b^2-2abcos(\angle between\ a\ and\ b)\\\\ a=2,78\\b=6,25\\ \angle between\ a\ and\ b=90+50=140^{\circ}\\\\ c^2=2,78^2+6,25^2-2*2,78*6,25cos(140^{\circ})\\\\ c^2=7,7284+39,0625-34,75*(-0,77)\\\\c^2=46,7909+26,7575\\\\c^2=735484\\\\c=8,58cm\\\\Total\ displacement\ is\ equal\ to\ 8,58cm.$