# Chapter 8 - Right Triangles and Trigonometry - Common Core Cumulative Standards Review - Selected Response - Page 540: 14

$AB \approx 42.2$

#### Work Step by Step

First, we want to know what angle is opposite the side in question. The angle that is opposite to the side we are looking for is $\angle C$, so let's plug in what we know into the formula for the law of cosines: $(AB)^2 = 32^2 + 15^2 - 2(32)(15)$ cos $124^{\circ}$ Evaluate exponents first, according to order of operations: $(AB)^2 = 1024 + 225 - 2(32)(15)$ cos $124^{\circ}$ Add to simplify on the right side of the equation: $(AB)^2 = 1249 - 2(32)(15)$ cos $124^{\circ}$ Take the square root of both sides to solve: $AB \approx 42.2$

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