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Bearings-Finding the angle of B as well as the finding the bearing from point A to Point C.

Cbarker1

Active member
Jan 8, 2013
236
Dear everyone,

An airplane flies 470 miles from point $A$ to point $B$ with a bearing of 25 degrees. It then flies from 250 miles from point $B$ to point $C$ with a bearing of 40 degrees. Find the distance and the bearing from A to point C.
Work

Bearing Problem.png
I understand that I need to use law of cosines for the side $b$ which is opposite of the angle $B$. But I have a hard time with find what is the angle $B$ is. I forgot many things from geometry. How to determine the angle from point $A$ to point $C$?

Thanks
Cbarker1
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
644
$AC = \sqrt{470^2+250^2 - 2(470)(250)\cos(165)}$

bearing = $25^\circ + m\angle{BAC}$

$\angle{BAC}$ may be found using either the sine or cosine law
 

Cbarker1

Active member
Jan 8, 2013
236
How did you determine the angle ABC to be 165?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
644
bearings.jpg