Answer
a) length of conduit:
$A_{1to2}+A_{2to3}+A_{3to4}+A_{4to5}+A_{5to6}=10ft+10.31ft+10ft+7.21ft+10ft=47.52ft$
b) straight-line distance:
$41.0~ft$
Work Step by Step
(a)
To find the length of the conduit, we add the blue segments.
We know all the horizontal values of the conduit but we do not know the diagonals.
The diagonals can be calculated as the hypotenuses of the right triangles they form with the measurements given in Illustration 8.
So, for segment $A_{2}$ to $ A_{3}$:
$a=4ft$
$b=9.5ft$
Using the Pythagorean Theorem
$A_{2to3}=\sqrt {a^{2}+b^{2}}=\sqrt {(4ft)^{2}+(9.5ft)^{2}}=10.31ft$
And, for segment $A_{4}$ to $ A_{5}$:
$a=4ft$
$b=15.5ft-9.5ft=6ft$
Using the Pythagorean Theorem
$A_{4to5}=\sqrt {a^{2}+b^{2}}=\sqrt {(4ft)^{2}+(6ft)^{2}}=7.21ft$
So, the length of conduit is
$=A_{1to2}+A_{2to3}+A_{3to4}+A_{4to5}+A_{5to6}=10ft+10.31ft+10ft+7.21ft+10ft=47.52ft$
(b)
The straight-line distance is the diagonal distance from the starting point (1) to the end point (6). This forms a right triangle with sides:
$10+4+10+4+10=38~ft$ and $15.5~ft$
Now, we find the hypotenuse with the Pythagorean Theorem:
$A_{1to6}=\sqrt {a^{2}+b^{2}}=\sqrt {(38ft)^{2}+(15.5ft)^{2}}=41.0~ft$
