Answer: 29 miles (approximate)
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Explanation:
Segment AB is already given to be 19 miles long.
I'm assuming your teacher meant to ask about side BC, which is side 'a' since it's opposite angle A.
Use the law of cosines to find the missing side
a^2 = b^2 + c^2 - 2*b*c*cos(A)
a^2 = 12^2 + 19^2 - 2*12*19*cos(138)
a^2 = 843.874040417691
a = sqrt(843.874040417691)
a = 29.0495101579647
a = 29 when rounding to the nearest whole number
Side BC is roughly 29 miles long.
