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Expert: - 8/19/2009


Question
a plane flies 500 km with a bearing of N 44 degrees W from B to C. The plane then flies 720 km from C to A. Find the bearing of the flight from C to A.

http://i763.photobucket.com/albums/xx275/trinhkieu888/9-1.jpg

this is the picture of this problem that my book gave me. Thank you!

Answer

Bearings
Questioner: T
Country: United States
Category: Advanced Math
Private: No
Subject: Pre-cal question
Question: a plane flies 500 km with a bearing of N 44 degrees W from B to C. The plane then flies 720 km from C to A. Find the bearing of the flight from C to A.

http://i763.photobucket.com/albums/xx275/trinhkieu888/9-1.jpg

this is the picture of this problem that my book gave me. Thank you!
.....................................................
Hi, T, (is that the name your mother calls you?)

Assuming the picture is accurate (see my version), then you want the obtuse angle (marked) at point C.

I have drawn the vertical line from C to S.

Now CS = 500 sin 46.  (compute that)
      = 359.67
And now use that to get the angle inside the left triangle.

cos(angle ACS) = CS/720.  (compute that)
angle ACS = arccos(CS/720)
         = arccos(0.49954)
         = 60.03 degrees.

Now 180 - angle ACS is your bearing, I believe.

(next time, don't hide behind a letter)

Paul Klarreich

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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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