Answer
The plane flew $78.9$ miles on the last leg of the trip.
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, $x$, is the angle that measures $60^{\circ}$, so let's plug in what we know into the formula for the law of cosines:
$x^2 = 57^2 + 90^2 - 2(57)(90)$ cos $60^{\circ}$
Evaluate exponents first, according to order of operations:
$x^2 = 3249 + 8100 - 2(57)(90)$ cos $60^{\circ}$
Add to simplify on the right side of the equation:
$x^2 = 11349 - 2(57)(90)$ cos $60^{\circ}$
Take the square root of both sides of the equation:
$x \approx 78.9$
The plane flew $78.9$ miles on the last leg of the trip.
