Surveying: in the surveying map shown below, calculate the distance and direction from point E to point A and estimate the enclosed area?

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1 Answer
Mar 21, 2018

#ae=72.0891#
#theta_(ae)=pi-tan^-1(72.0881/0.3893)#

Explanation:

#ab=40#
#theta_(ab)=0#
#x_(ab)=40cos0=40#
#y_(ab)=40sin0=0#

#bc=30#
#theta_(bc)=-pi/4#
#x_(bc)=30cos(-pi/4)=21.2132#
#y_(bc)=40sin0=-21.2132#

#cd=50#
#theta_(cd)=pi/3#
#x_(cd)=50cos(pi/3)=25#
#y_(cd)=50sin(pi/3)=43.3013#

#de=100#
#theta_(de)=(5pi)/6#
#x_(de)=100cos(5pi)/6=-86.6025#
#y_(de)=100sin(5pi)/6=50#

#x_(ae)=x_(ab)+x_(bc)+x_(cd)+x_(de)#
#=40+21.2132+25-86.6025#
#x_(ae)=-0.3893#
#y_(ae)=y_(ab)+y_(bc)+y_(cd)+y_(de)#
#=0-21.2132+43.3013+50#
#y_(ae)=72.0881#

#ae=sqrt(x_(ae)^2+y_(ae)^2)#
#ae=72.0891#
#theta_(ae)=tan^-1(y_(ae)/(x_(ae)))#
#=tan^-1(72.0881/-0.3893)#
#theta_(ae)=pi-tan^-1(72.0881/0.3893)#