SOLUTION: 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

Question 194865: 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?
Is there a formula I have to follow? Thank you in advance.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
a = 37 mi apart
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