Problem #$5$: Horizontal Curves $(15$ points$)$

A pipeline is defined by a series of tangential lines between points J$-$K$-$L$-$M$-$N as follows:

$\backslash$table$[[$Course$,$Length $($straight line$)],[$JK$,830\mathrm{.}00],[$KL$,965\mathrm{.}00],[$LM$,1210\mathrm{.}00],[$MN$,1750\mathrm{.}00]]$

The first horizontal curve $($connecting lines $JK$ and $KL)$ has a radius of $400\mathrm{.}00$ feet and an internal angle of $66{10}^{\text{'}}{30}^{\text{'}\text{'}}.$ The second horizontal curve $($connecting lines KL and LM$)$ has a radius of $600\mathrm{.}00$ feet and an internal angle of $43{42}^{\text{'}}{15}^{\text{'}\text{'}}.$ The third horizontal curve $($connecting lines LM and MN$)$ has a radius of $500\mathrm{.}00$ feet and an internal angel of $51{25}^{\text{'}}{48}^{\text{'}\text{'}}.$ Determine the total length of the pipeline between joints $J$ and $N$ incorporating horizontal curves.

A piping configuration in a manufacturing plant is shown in the figure below. Assume that lines $AB$ and $CD$ are Due East. Assume that lines $BC$ and $DE$ are Due North. Using the data provided in the figure, determine the total actual length of the pipe $($shown in a solid line$)$ between points A and E$.$ All coordinates $(x,y)$ provided are in feet.

dist $A-B=205-55=150$

dist $B-C=230-135=95$

dist $C-D=205-100$:${105}^{\text{'}}$

dist $E-D=200-135={65}^{\text{'}}$

Length $={150}^{\text{'}}-{30}^{\text{'}}+{47\mathrm{.}1}^{\text{'}}+{95}^{\text{'}}-({30}^{\text{'}}2)+{471}^{\text{'}}$

$+{105}^{\text{'}}-({30}^{\text{'}}2)+47\mathrm{.}1+65-30+47\mathrm{.}1$

Please solve for problem #$5.$ There are two other images that is a similiar problem to #$5.$ Please look at the example problem and solve #$5$ like the example problem. PLEASE do what is asked. use the steps provided in the example problem to solve for #$5$ exactly. thank you.