# Bearings of a Point

Let

*EW*be a line in the eastâ€“west direction and*NS*be a line perpendicular to it in the northâ€“south direction. Let the two lines intersect at*O*. Let*P*be any point. The acute angle which*OP*makes with*NS*is called the bearing of the point*P*from*O*. The bearing of a point is briefly indicated by giving the size of the acute angle and specifying whether it is measured from*ON*or*OS*and whether to the east or west.*OA*is in the direction 60Â° east of north and the bearing of*A*is written as*N*60Â°*E*.*OB*is in the direction 30Â° west of north and the bearing of*B*is written as*N*30Â°*W*.*OC*is in the direction 40Â° west of south and the bearing of*C*is written as*S*40Â°*W*.*OD*is in the direction 75Â° east of south and the bearing of*D*is written as*S*75Â°*E*.

*m* â€“ *n* Theorem

(

*m*+*n*) cot*Î¸*=*m*cot*Î±*â€“*n*cot*Î²*=

*n*cot*A*â€“*m*cot*B*(*Î¸*on the right)If

*Î¸*is on the left then angle in the right is*Ï€*â€“*Î¸*and cot (*Ï€*â€“*Î¸*) = â€“ cot*Î¸*. Hence in this case*m*â€“*n*theorem becomes â€“ (*m*+*n*) cot*Î¸*=*m*cot*Î±*â€“*n*cot*Î²*=*n*cot*A*â€“*m*cot*B*(*Î¸*on the left)