# trig

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A plane has an airspeed of 200 miles per hour and a heading of 28.0°. The ground speed of the plane is 207 miles per hour, and its true course is in the direction of 38.0°. Find the speed and direction of the air currents, assuming they are constants. (Round your answers to one decimal place.)
_____mi/hr at ____° from due north

• trig - ,

I assume you are studying vectors.

Draw a line at 28° of length 200 (your resultant)
Draw a line at 38° of length 207, join its tail to the first line.
That smaller line will be the vector representing the wind

I see a triangle with sides 200 and 207, with a contained angle of 10°
Let the length of the smaller side be x

by cosine law:
x^2 = 200^2 + 207^2 - 2(200)(207)cos10°

etc.

x will be you speed of the wind, and from your diagram it should be straightforward to find the wind direction

• trig - ,

I got calculated 36.1 to one decimal point. And the wind direction I believe should be 200. Do not trust my answer. Thanks!