Try to doodle a triangle of forces and find that the greatest and least resultants occur when the two forces (x,y) are colinear. When they are additive, we have x+y=17 kN, and when they oppose each other, we have x-y=5 (if x>y).
Thus solution of the system of equations yields
x=(17+5)/2=11
y=(17-5)/2=6
Going back to the triangle of forces for the resultant (z=√(144)=12), we have the relationship among x, y and z defined by the cosine rule, namely,
z²=x²+y²-2xy(cos(θ))
from which you can solve for θ=84° approx.
the greatest and least resultant of two forces are respectively 17 KN and 5 KN. determine the angle between two force when their resultant is root 144 KN.
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