Often a good idea to draw a very quick and **rough sketch** to give you an idea of what you are having to deal with.

Set #rarr# as positive thus #larr# is negative

Set #uarr# as positive thus #darr# is negative

#color(brown)("Consider the horizontal")#

#AB_h=+[7.4xxsin(45^o)]~~+5.23159..#

#BC_h=+[2.8xxcos(30^o)]~~+2.42487..#

#CD_h=-[5.2xxsin(22^o)]~~-1.94795..#

Sum #~~+5.70950....#

#color(brown)("Consider the vertical")#

#AB_h=+[7.4xxcos(45^o)]~~-5.23259.....#

#BC_h=+[2.8xxsin(30^o)]=+1.4" "...#

#CD_h=-[5.2xxcos(22^o)]~~+4.82135...#

Sum #~~+0.98876....#

So we end up with:

#beta =tan^(-1)(0.988765...)/(5.709507..)~~9.82497..."degrees East North"#

#"Resultant "r ~~ sqrt((0.988765..)^2+(5.709507..)^2)#

#r=5.794491212bar(12)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("This is a repeating decimal so a rational number")#

#color(brown)("Converting to an exact fractional answer")#

Set #x_1=5.794491212bar(12)#

Set#x_2=0.794491212bar(12) #

#10000000x_2=7944912.1212bar(12)#

#ul(color(white)("d0")100000x_2=color(white)("00")79449.1212bar(12)larr" Subtract")#

#color(white)("d")9900000x_2=7865463#

#x_2=7865463/9900000#

#r=x_1 = 5 color(white)("d")7865463/9900000 color(red)(larr" What an awful number!!!")#

#color(red)("I'm sticking with the decimal!!")#