SOLUTION: To widen a road, a tree stump needs to be removed. Two backhoes are brought to the site. One backhoe pulls with a force of 2500 N east while the second backhoe pulls with a force o

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Question 1044189: To widen a road, a tree stump needs to be removed. Two backhoes are brought to the site. One backhoe pulls with a force of 2500 N east while the second backhoe pulls with a force of 3000 N northeast. What is the resultant force and its angle with respect to the first backhoe?
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Answer by Alan3354(69443) About Me  (Show Source):
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To widen a road, a tree stump needs to be removed. Two backhoes are brought to the site. One backhoe pulls with a force of 2500 N east while the second backhoe pulls with a force of 3000 N northeast. What is the resultant force and its angle with respect to the first backhoe?
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The angle between the 2 lines is 22.5 degs
The resultant is the 3rd side of a triangle with sides of 2500 and 3000, and the included angle = 180 - 22.5 = 157.5 degs
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r^2 = 2500^2 + 3000^2 - 2*2500*3000*cos(157.5)
r^2 =~ 29108193
r=~ 5395.2 N
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Find the cosine of the angle between the resultant and North:
3000^2 = r^2 + 2500^2 - 2*2500*r*cos(R)
cos(R) =~ 0.977
R = 12.3 degs