SOLUTION: Jan is flying a plane 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 exactl
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Question 327992: Jan is flying a plane 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? Found 2 solutions by Fombitz, Edwin McCravy:Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Rate*Time=Distance
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For the two hours she traveled 640 miles East or (640,0) on a coordinate grid.
She is currently traveling at a rate of (320cos(65),-320sin(65)).
When she's exactly southeast,
where
Substituting, hrs
You can put this solution on YOUR website! Jan is flying a plane 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?
Let the black line in the drawing below represent her path.
She starts out at A, flies for 2 hours at 320 mi/h from A to B.
That's 640 miles, so AB = 640 miles. Then she turns at a 65°
angle and flies to C. The problem asks to find the time it took
her to fly from B to C.
Now in order for point C to be exactly southeast of A, the red line
AC must make a 45° with AB, so we have this:
Angle ABC is supplementary to the 65°-angle, so it's 180°-65°=115°.
Since the three angles of triangle ABC must have sum 180° we can
calculate angle C as 180°-(45°+115°) = 20°, so we indicate the
measures of those two angles:
What we're looking for is how long it took her to fly from
B to C. So let's first calculate BC using the law of sines:
.
Now we use to find
the time it took her to fly the 1323.162828 miles from B to C.
or about 4 hours and 8 minutes.
Edwin
