# Chapter 11 - Section 11.4 - Applications with Acute Triangles - Exercises - Page 528: 29a

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.

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