An airplane flies 180 miles from point A in the direction 120 degrees and then travels 210 degrees for 80 miles. Approximately how far is the airplane from point A?

I know that I will need to use the law of cosine. distance^2= a^2+b^2-2abcos?
I am not sure how to find the angle
An explanation of how to draw the triangle would be great!

asked by Meranda
  1. you could resolve the two legs into north-south and east-west components, and add them

    posted by scott
  2. Like an x and y-axis?

    posted by Meranda
  3. Would the angle between the two sides be 150 degrees? If not, then I need more explanation.

    posted by Meranda
  4. Disp. = 180mi[120o] + 80mi[210o].

    X = 180*sin120 + 80*sin210 = 115.9 Mi.
    Y = 180*Cos120 + 80*Cos210 = -159.3 Mi.

    Disp. = Sqrt(X^2+Y^2).

    posted by Henry
  5. We haven't learned about dispositions yet so I don't think that's how I am supposed to solve it

    posted by Meranda
  6. Anybody else that can help me with this?

    posted by Meranda
  7. Disp. = Displacement which is the straight line distance from the starting point (A) to the
    destination. I used vector analysis and trig to solve it. The only remaining method is
    The Law of Sine and Cosines.

    posted by Henry

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