# Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 322: 52

The horizontal distance between point A and point B is 18 feet.

#### Work Step by Step

Let $a = 10~ft$, let $b = 10~ft$, and let angle $C = 128^{\circ}$. We can use the law of cosines to find $c$, the length of the line opposite the angle $C$: $c^2 = a^2+b^2-2ab~cos~C$ $c = \sqrt{a^2+b^2-2ab~cos~C}$ $c = \sqrt{(10~ft)^2+(10~ft)^2-(2)(10~ft)(10~ft)~cos~128^{\circ}}$ $c = \sqrt{323.13~ft^2}$ $c = 18~ft$ The horizontal distance between point A and point B is 18 feet.

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