#### Answer

AB has a length of 257 m

#### Work Step by Step

We can use the law of cosines to find the length $AB$:
$AB^2 = AC^2+BC^2-2(AC)(BC)~cos~C$
$AB = \sqrt{AC^2+BC^2-2(AC)(BC)~cos~C}$
$AB = \sqrt{(350~m)^2+(286~m)^2-(2)(350~m)(286~m)~cos~46.3^{\circ}}$
$AB = \sqrt{65981.34~m^2}$
$AB = 257~m$
AB has a length of 257 m