The resultant vector is known to have made a 6.3-degree angle with the horizontal force, hence correct option is A.
How do you determine angle of the resultant vector ?
The resultant angle between the vectors is given by
θ = [tex]tan ^{-1}[/tex] = [tex]\frac{B sin θ}{A + B cos θ}[/tex]
Note that the two forces are said to have the magnitude of 17.3 and 42.5 pounds hence, the angle of the resultant vector is known to be:
[tex]θ = tan^{-1} = \frac{17.3 sin 21. 9}{42.5 + 17.7 cos 21.9 }[/tex]
= (6.453/58.55)
= 6.2886 degree
= 6.3 degree.
Therefore, in the above scenario, the resultant vector makes a 6.3-degree angle with the horizontal force.
See full question below
Two forces of 17.3 pounds and 42.5 pounds act on a body with an angle of 21.9 degrees between them. The force of 42.5 pounds acts on the body in the horizontal direction. Choose the correct approximation for the direction angle the resultant vector makes with the horizontal force.
a. 6.3
b. 21.9
c. 15.7
d. 10.9
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