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Hi I need help with this problem can anyone please help me and please make it...

Hi I need help with this problem can anyone please help me and please make it clear with step by step solution and please make it clear to read thank you please make sure the answer is correct thankyou

Three forces with magnitudes of 51 pounds, 100 pounds, and 129 pounds act on an object at angles of 30°, 45°, and 120° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. (Round your answers to one decimal place.)

direction   °
magnitude   lb
science   physics   
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Answer #1

The three vectors can be written as
(51cos (30), 51sin (30)) = (44.167, 25.5)
(100cos 45, 100sin45), = (70.711, 70.711)
(129cos120, 129sin120) = (-64.5, 111.717)

So the sum of those three vectors is
(50.378, 207.928)

The magnitude of that is
√ (50.3782 + 207.9282) = 213.9

The direction would be arctan(207.928/50.378) = 76.4°

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