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TheUppercut
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Homework Statement
An airplane is traveling with airspeed of 225 mph at a bearing of 205 degrees. A 60 mph is blowing with a bearing of 100 degrees. What is the resultant ground speed and direction of the plane?
Homework Equations
x = u cos(degrees)
y = v sin(degrees)
However, I think the solution needs to be found by using the Law of Cosines and the Law of Sines.
Law of Cosines: c^2 = a^2 + b^2 - (2)(a)(b)(cos(C))
Law of Sines: (sin(a)/A) = (sin(b)/B)
The Attempt at a Solution
I was able to find the solution by using the first method, but not by using the Law of Cosines.
First method:
x = 225 cos(205) + 60 cos(100) = -214.338 --> -214.338^2 = 45940.839
y = 225 sin(205) + 60 sin (100) = -36 --> -36^2 = 1296
x^2 + y^2 = 45940.839 + 1296 = 47236.839 --> sqrt(47236.839) = 217, which is the ground speed
I then found the bearing by taking the tan(y/x), then arctan of that answer. So, (-36/-214.338) = .16796 --> arctan(.16796) = 9.53, which has to be added to 180, to get the bearing of 189.53
With the Law of Cosines and Law of Sines, I am completely stumped. I have tried drawing a diagram with the bearings and then using the Law of Cosines to find the resultant, but no such luck. Any help would be greatly appreciated!
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