Following+a+Plane+Bearing

Mallory Beard Dan Eckman Ellen Bowman

=Following a Plane Bearing =

=** Problem: **= __ Solving For Angles __
 * A plane takes off with a bearing of 34 degrees east of north. After 67 miles it changes its bearing to 28 degrees west of north and travel for 43 miles. 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.**

To find the 56-degree angle, we added 90 and 34 to find 124. Then we subtracted 124 from 180.

To find the 118- degree angle, we added 28 and 34 together to get 62. Then, we subtracted 62 from 180.

Finally, to find the other 28-degree angle, we added 118 and 34 to get 152. Then, we subtracted 152 from 180.

__ Trig Function Usage __

We used Trig functions to determine the bearing and displacement of the plane. The bearing was 37 degrees Northeast and the displacement from the original starting point was 95.1 miles. To find this, we used the Law of Cosines for both. Law of Cosines is C^2= A^2+B^2 - 2AB(cosc)

Calculating Plane Bearing:  C^2=A^2+B^2-2AB(cosc)   43^2=(67^2+95^2)-2(67)(95)x(cosc)   1849=11714-2(67)(95)x(cosc)   -9865=-2(67)(95)x(cosc)   -9865=-12350x(cosc)   .799=cosc   inverse cos(.799)=c   c=37 degrees NE

note: angle c is labeled as 34 degrees on the diagram. this is a mistake, the correct label is 37 degrees.

Calculating side C   C^2=A^2+B^2-2AB(cosc)c^2=67^2+43^2-2(67)(43)x(cos118)C^2=9043.09C=95.1 miles