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**HallsofIvy** Start by drawing a picture. Draw a line at 105° and label it "100 km". Call that "D" (the "D"irect line to the "D"estination). Draw a second line,, starting at the same initial point, at 210° and label it "20t km" (t is the time in hours). Call that "W" ("W"ind). Finally, draw the line connecting the ends to form a triangle. That line represents a vector that, added to "W" gives "D". Call that "P" (for "P"lane).

Now, there are two ways to find length and direction of "P". One is to find "x" and "y" components for vector "D" and "W". You want P+ W= D (the motion of the plane plus the motion of the wind takes the plane along the correct route) so that P= D- W. Subtract corresponding components of D and W to get the components of P.

Or, my preference, "solve the triangle. You have two adjacent sides of lengths 100 and 20t with angle between them 210- 105= 105°. You can use the "cosine law" to find the length of the third side of the triangle (the length of vector P in terms of t so that the coefficient of t is the speed of the airplane) and then use, say, the sine law to determine the angle.