#### Answer

BC has a length of 25.24983 miles

#### Work Step by Step

We can use the law of cosines to find the length $AB$:
$BC^2 = AB^2+AC^2-2(AB)(AC)~cos~A$
$BC = \sqrt{AB^2+AC^2-2(AB)(AC)~cos~A}$
$BC = \sqrt{(22.47928~mi)^2+(28.14276~mi)^2-(2)(22.47928~mi)(28.14276~mi)~cos~58.56989^{\circ}}$
$BC = \sqrt{637.5539346388~mi^2}$
$BC = 25.24983~mi$
BC has a length of 25.24983 miles