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A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 690 mi/h, how far is she from her starting position

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opudodennis

Answer:

2406 miles

Explanation:

Let A be the starting position, B the junction position and C the final position after flying the 3.5 hrs. Also, let b be the distance from the starting point:

[tex]\angle ABC =(180-10) \textdegree=170\textdegree[/tex]

#Distance traveled in 1.5hrs is;

[tex]c=690x1.5\\=1035mi[/tex]

#Distance traveled in next two hrs:

[tex]a=690\times 2\\=1380mi[/tex]

#Now using the Cosine Rule:

[tex]b^2=a^2+c^2-2ab\cos B\\\\=1380^2+1035^2-2(1380)(1035)cos170\textdegree\\\\b^2=5788.83\\\\b\approx 2406.00 \ mi[/tex]

Hence, the pilot is 2406 miles from her starting position.