Question 160302
</pre><font size=4><b>
As you can sketch they form a right triangle ---> Ship1 goes East and Ship2 goes South with 17 miles apart (hypotenuse).
Then, {{{S[2]}}} is {{{x}}} miles fromt the port. (adjacent), that depends of course which angle of inclination. For argument sake we put adjacent.
Also, {{{S[1]}}} is {{{7+x}}} miles farther from the port than {{{S[2]}}} (opposite)
By Pythagorean Theorem:
{{{hyp^2=adj^2+opp^2}}} --------------> working eqn
{{{17^2=x^2+(x+7)^2}}}
{{{x^2+x^2+14x+49-289=0}}}
{{{2x^2+14x-240=0}}} divide whole eqn by 2
{{{x^2+7x-120=0}}} perfect square
{{{(x+15)(x-8)=0}}}
{{{x=-15}}}, {{{x=8}}}
use {{{x=8miles}}}, distance of {{{S[2]}}} from the port
{{{7+8=15miles}}}, distance of {{{S[1]}}} from the port
check via working eqn:
{{{17^2=8^2+15^2}}}
{{{289=64+225}}}
{{{289=289}}}
Thank you,
Jojo</pre.