Question 1125558




Find the speed of the 1st boat (s)

{{{s/18}}} = {{{sqrt(3)/2}}}....cross multiply 
{{{2s = 18*sqrt(3)}}}
{{{s = 31.177/2}}}
{{{s = 15.6 (km/h)}}} is the speed of the 2nd boat


Find the distance each has traveled in {{{5}}} hrs

{{{5*15.6 = 78km}}} traveled by the 1st boat
{{{5*18 = 90km}}} by the 2nd boat


The distance between the boat is the side (a) opposite the 30 degree angle (A)
Use the law of cosines: 

{{{a^2 = b^2 + c^2 - 2bc*Cos(a)}}},where
{{{b = 78}}}
{{{c = 90}}}
{{{a^2 = 78^2 + 90^2 - 2(78*90)*Cos(30)}}}

{{{a^2 = 6084 + 8100 - 2(7020)*.866}}}

Do the math
{{{a = sqrt(2025)}}}
{{{a = 45km}}} apart in 5 hrs


so, answer is A){{{45}}}