Answer
The length of the remaining side is $x = 213.4$ ft.
Work Step by Step
1. Use the Law of Cosines to find the length
Let $x = $ the length of the remaining side of the lot
$x^{2} = a^{2} + b^{2} - 2abcos(C)$
$x^{2} = (180)^{2} + (150)^{2} - 2(180)(150)cos(80)$
$x^{2} = 32400 + 22500 - 54000cos(80)$
$x^{2} = 54900 - (9377.001594)$
$x^{2} = 45522.99841$
$x = ±\sqrt {(45522.998...)}$
$x = ±213.3611...$ ft
$x \approx ±213.4$ ft
Since $x \ne -213.4$ ft, then $x = 213.4$ ft.
