Question 312879
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The paths of the two aircraft are *[tex \Large 135^\circ] apart.  So we have a triangle with sides of *[tex \Large 600\ \times\ 2\ =\ 1200] km and *[tex \Large 400\ \times\ 2\ =\ 800] km and an included angle of *[tex \Large 135^\circ].


Use the Law of Cosines:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ \sqrt{a^2\ +\ b^2\ -\ 2ab\cos{C}}]


Since similar triangles have proportional sides, to save some arithmetic difficulties, I recommend using 12 and 8 for the measures of the sides and then multiplying the result by 100 to re-scale your triangle.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ \sqrt{12^2\ +\ 8^2\ -2(12)(8)(-\frac{\sqrt{2}}{2})}]


You can run a calculator as well as I can -- the rest is up to you.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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