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Two tow trucks try to pull a car out of a ditch.One tow truck applies a force
of 1,500 pounds while the other truck applies a force of 2,000 pounds. The
resultant force is 3,000 pounds. Find the anlge between the two forces, rounded
to the nearest degree.
Draw the two vector forces and their resultant and the parallelogram:
Isolate the upper triangle and label it ABC with sides a,b, and c::
Solve for angle A using the law of cosines
Find the inverse cosine:
A = 117° to nearest degree
Now back to the vector drawing:
Angle A, however, is not the angle between the forces. But we notice by
removing the resultant 3000# vector:
that, since two adjacent angles of a parallelogram are supplementary,
we only need to subtract 117° from 180° and get 63°, the angle between
the two forces: