Trig

posted by Meranda

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!

  1. scott

    you could resolve the two legs into north-south and east-west components, and add them

  2. Meranda

    Like an x and y-axis?

  3. Meranda

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

  4. Henry

    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).

  5. Meranda

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

  6. Meranda

    Anybody else that can help me with this?

  7. Henry

    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.

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