SOLUTION: <p>Two forces <strong>429 N</strong> and <strong>591 N</strong> act on an object. The angle between the forces is <strong>46&deg;</strong>. Find the <span style="text-decoration: u

Algebra ->  Trigonometry-basics -> SOLUTION: <p>Two forces <strong>429 N</strong> and <strong>591 N</strong> act on an object. The angle between the forces is <strong>46&deg;</strong>. Find the <span style="text-decoration: u      Log On


   



Question 1102869:

Two forces 429 N and 591 N act on an object. The angle between the forces is 46°. Find the magnitude of the resultant and the angle that it makes with the larger force.


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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a representation of the two forces and their resultant,
R :

The rest is trigonometry.
You could use law of cosines and law of sines,
but I would favor just calculating the horizontal and vertical components.
The 429N force can be seen as the sum of
a horizontal component of magnitude cos%2846%5Eo%29%2A429N=about+298.0N , and
a vertical component of magnitude sin%2846%5Eo%29%2A429N=about+308.6N .
The 591N force an be seen as the sum of
a horizontal component of magnitude 591N , and
a vertical component of magnitude 0N .
Adding up components, you get the horizontal and vertical components,
R%5Bx%5D=298.0N%2B591N=889.0N and R%5By%5D=308.6N%2B0N=308.6N
tan%28theta%29=R%5By%5D%2FR%5Bx%5D=308.6N%2F%22740.0+N%22=0.3341 --> theta=19.1%5Eo .
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