Question

PLEASE HELP!!!!!!

Two ships, A and B, set sail from the same port. Ship A traveled in a northwesterly direction such that its path formed a 50° angle with the line for due north. Ship B traveled due east from the port. What is the distance, d, between the ships when Ship A has traveled 12 miles on its path and Ship B has traveled 10 miles on its path?

9.5 miles
20.0 miles
20.7 miles
22.0 miles

Answer 1

20.7 correct rounding for odyssey

Explanation:

Answer 2

`\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\ -----------------------------\\\\ \begin{cases} a=12\\ b=10\\ D=90+50 \end{cases}\implies d = \sqrt{{{ 12}}^2+{{ 10}}^2-2(12)(10)cos(140^o)} \\\\\\ d\approx √(427.851)\implies d\approx 20.684551`