Answer
The length of the property line is 47.5 feet
Work Step by Step
Let $a = 13.0~ft$, let $b = 14.0~ft$, and let angle $C = 70.0^{\circ}$.
We can use the law of cosines to find $c$, the length of the line opposite the angle $C$:
$c^2 = a^2+b^2-2ab~cos~C$
$c = \sqrt{a^2+b^2-2ab~cos~C}$
$c = \sqrt{(13.0~ft)^2+(14.0~ft)^2-(2)(13.0~ft)(14.0~ft)~cos~70.0^{\circ}}$
$c = \sqrt{240.5~ft^2}$
$c = 15.5~ft$
The distance of the missing section is 15.5 feet.
We can find the length of the property line between the two markers:
$18.0~ft+15.5~ft+14.0~ft = 47.5~ft$
The length of the property line is 47.5 feet
