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Problem Seven- Following a Plane Bearing

A plane takes off with a bearing of 32 ̊east of north. After 65 miles it changes its bearing to a 28 ̊ west of north and travels for 43. Plot the course of the plane with all angles shown, determine its displacement from the starting point, and determine the bearing from the starting point.

1. First you label the sides accordingly by what the problem says.

2. You use the law of interior angles to find the other 32 degree angle.

3. Then you use the law of cosines to figure out the displacement- which is 94.2 miles

C^2=43^2+65^2-2*43*65*cos(120 ̊) C^2=1849+4225-5990*cos(120 ̊) C^2=6074+2795 √c^2=√8869 C=94.2 miles

4.To find the bearing you need to find the angle between the north and south line and the displacement line. You use law of interior angles again and find the 28 degree angle. You need to find one more angle in the triangle so that you can use the fact that there is 180 degrees in a triangle. You use the law of sines to find this other angle.

Sin(120 ̊)/94.2=sin(x)/65 65sin(120 ̊)/94.2=94.2sin(x)/94.2 Sin(x)=65sin(120 ̊)/94.2 Sin(x)=.60 X=36.7 ̊

5. You take 36.7 degrees and subtract it from 180 degrees to find that this angle is 143.3 degrees. After that you add 28 degrees and 143.3 degrees and subtract that from 180 degrees. You get 8.7 degrees. Therefore the bearing is 8.7 degrees East of North.  Displacement-94.2 miles Bearing-8.7 degrees East of North

Seth Nate Nate Jess