# Calculus

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Two forces, F1 and F2 act on an object and the angle between them is 60 degrees. Determine the magnitude and the direction of the resultant force FR relative to F1 if F1= 50 N and F2= 30 N.

• Calculus -

Did you make a diagram?
I drew the 20 N line, and at its end drew the 50 N line with an angle of 120° between them.
(you should be familiar with the parallelogram resulting from the addition of 2 vectors with the diagonal representing the resultant R)

|R|^2 = 50^2 + 20^2 - 2(50)(20)cos 120°
= 2500 + 400 - 2000(-1/2)
= 3900
|R| = √3900 = appr. 62.45 N

now you can use the Sine Law to find the angle between either vector and the resultant.

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