SOLUTION: You and your friend’s tugboats are 120 ft apart, and you’re pulling the same barge. The length of the cable from your tugboat to the barge is 212 ft, and the length of your friend’

Question 141856: You and your friend’s tugboats are 120 ft apart, and you’re pulling the same barge. The length of the cable from your tugboat to the barge is 212 ft, and the length of your friend’s cable is 230 ft. What is the angle formed by your two cables?
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(5880) (Show Source):
You can put this solution on YOUR website!
let x=angle

by the law of cosines __ cos(x)=(212^2+230^2-120^2)/(2(212)(230))

cos(x)=.856 (approx.)

x=31.2° (approx.)

Answer by stanbon(48526) (Show Source):
You can put this solution on YOUR website!
You and your friend’s tugboats are 120 ft apart, and you’re pulling the same barge. The length of the cable from your tugboat to the barge is 212 ft, and the length of your friend’s cable is 230 ft. What is the angle formed by your two cables?
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Draw the triangle that is formed by the two ropes and the distance between
the tugs.
The angle you want is opposite the 120 ft. distance between the tugs.
Use the Law of Cosines to find the angle:
cos(A) = (b^2+c^2-a^2)/2bc
cos(A) = (212^2 + 230^2-120^2)/(2*212*230) = 0.85566
A = cos^-1(0.85566) = 31.167 degrees
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Cheers,
Stan H.