Final answer:
The angle between two cables pulling an object from above is determined by solving for the arccosine of the dot product of the force vectors divided by the product of their magnitudes, and then rounding to the nearest degree.
Step-by-step explanation:
The student is asking to determine the angle between two cables pulling an object from a point above. The forces are given as force vectors for each cable: F1 = −78i + 44j and F2 = 87i + 80j. To find the angle between the two cables, we can use the dot product formula, which in two dimensions is given by F1 · F2 = |F1| |F2| cos(θ), where θ is the angle between the vectors and |F1| and |F2| are the magnitudes of F1 and F2, respectively.
To find the magnitudes of F1 and F2, we use the formula |F| = √(i^2 + j^2) for each force vector, where i and j represent the components of the vectors in the respective directions. After calculating the magnitudes, the angle θ can be found by solving for cos(θ) = (F1 · F2) / (|F1| |F2|) and then computing the arccosine θ = arccos((F1 · F2) / (|F1| |F2|)). Round the result to the nearest degree to get the angle between the cables.
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