Question 146543: I am having a problem understanding where the answer is coming from in this question. Any assistance would be appreciated. The question is, a plane flies at a bearing due east from the airport for 120 km. It changes directon to 30 degrees and then travels and additional 50 km. How far is the plane from the airport. I used the Law of Cosines of c^2 = a^2 + b^2 - 2abCosC. Which I used a = 50 and b = 120. Cos C = 30 degrees. So my final answer is 2500 + 14,400 - 2(50)(120)*.8666 = 6500. a^2 = 6500 = 80.62 km.
But the answer says I should be using a^2 = b^2 + c^2-2bc CosA. They use 120 for b and 50 for C and 120 degrees for Cosine A. Answer is 151 km. Please advise why I am to be using Cos 120 and not Cos30. I am reading if it says it changes direction to 30 degrees, not just 30 degrees, that it is going north towards 30 degrees, Perhaps this is not correct. Thank you.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 120 degs is the angle between the 2 headings.
"Due East" is a heading of 090. If you draw that, then draw a line from the end of it heading 030, you'll see that. It's a change of direction of 60 degs, but the internal angle is 120.
A heading of 030 is 30 degs "to the right" of vertical.
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