Question

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

Answer 1

`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)`