SOLUTION: Jan is flying on a triangular course at 320 mi/h. She flies due east for two hours and then turns right through a 65 degree angle. How long after turning will she be exactly southe

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Question 328202: Jan is flying on a triangular course at 320 mi/h. She flies due east for two hours and then turns right through a 65 degree angle. How long after turning will she be exactly southeast of where she started?
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
There are various ways to go about this one. Here is one method.
From where she makes her 65 degree turn, extend a line straight out, then connect it to the point where she intersects the southwest line.
This forms a right triangle. Draw a line from the intersection point back to where she turned. This forms another triangle.
Let the distance extended out from where she turned be x and the distance from there to the intersection point be 640+x (because southeast is 45 degrees from the origin)
The distance she flies is 320t.
Now, we can build two triangles and solve for t and x. t is what we really need.
sin%2825%29=x%2F320t
x%5E2%2B%28640%2Bx%29%5E2=%28320t%29%5E2....[2]
x=320t%2Asin%2825%29....[3]
Sub [3] into [2] and solve for t.
%28320t%2Asin%2825%29%29%5E2%2B%28640%2B%28320t%2Asin%2825%29%29%29%5E2=%28320t%29%5E2
204800sin%5E2%2825%29%2At%5E2%2B409600sin%2825%29t%2B409600=102400t%5E2
This is a quadratic to solve for t.
Doing so, gives us t=4.13 hours.
The other solution is extraneous.