<PRE><B>Question 194865</B>
Two ships leave harbor at the same time. 
The first sails North 15 degress West at 25 knots. 
The second sails North 32 degress East at 20 knots. 
After 2 hours, how far apart are the ships?
:
From the given headings we can say the angle between the courses of the two ships:
15 + 32 = 47 degrees
:
After two hrs 
the 1st ship will have traveled 2*25 = 50 mi
the 2nd ship will have traveled 2*20 = 40 mi
:
We can use the law of cosines for a side/angle/side problem
a^2 = b^2 + c^2 - (2bc * cos(A))
:
Assign the values as follows
a = distance between ships after 2 hr (side opposite angle A)
b = 50
c = 40
A = 47 degrees
:
a^2 = 50^2 + 40^2 - (2*50*40 * cos(47))
a^2 = 2500 + 1600 - (4000*.682)
a^2 = 4100 - 2728
a^2 = 1372
a = {{{sqrt(1372)}}}
a = 37 mi apart</PRE>