SOLUTION: An airplane starting from airport A,flies 300km east, then 350km 30°west of North, and then 150km north to arrive at airport B. Assuming that there was no wind on that day,
a) de
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Question 1206227: An airplane starting from airport A,flies 300km east, then 350km 30°west of North, and then 150km north to arrive at airport B. Assuming that there was no wind on that day,
a) determine in what direction should the pilot fly to travel directly from A to B?
b) How far will the pilot fly to travel directly from A to B?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
from point A, he goes east 300 kilometers.
then he goes on a bearing of 30 degrees west of north for 350 kilometers.
breaking this down to east/west and north/south directions, you get:
west direction = 350 * sin(30) = east 175 kilometers.
north direction = 350 * cos(30) = north 303.1088913 kilometers.
then it's 150 kilometers in a north direction.
total east west direction = 300 kilometers east minus 175 kilometers west = 125 kilometers east.
total north south direction = 303.1088913 kilometers north plus 150 kilometers north = 453.1088913 kilometers north.
this forms a right triangle ABC where AC = 125 kilometers and BC = 453.1088913 kilometers.
the hypotenuse of this triangle is equal to AB which is equal to sqrt(125^2 + 453.1088913^2) = 470.0347512 kilometers.
that's the direct distance from A to B.
the direction of travel is arccos(125/470.0347512) = 74.5773165 degrees.
90 minus that = 15.4226835 degrees.
point B is 15.4226835 degrees east of north from point A.
here's my diagram.
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