Step 1 :Given two forces of 488 newtons and 501 newtons acting on a point, with a resultant force of 953 newtons, we are to find the angle between the two forces.
Step 2 :This problem involves the concept of vector addition and the law of cosines. The resultant force is the vector sum of the two forces. The law of cosines can be used to find the angle between the two forces.
Step 3 :The law of cosines states that for any triangle with sides of lengths a, b, and c and an angle γ between sides a and b, the following equation holds: \(c² = a² + b² - 2ab \cos(γ)\)
Step 4 :In this case, a and b are the magnitudes of the two forces, c is the magnitude of the resultant force, and γ is the angle between the two forces. We can rearrange the equation to solve for \(\cos(γ)\) and then use the arccos function to find γ.
Step 5 :Let a = 488, b = 501, and c = 953. Substituting these values into the law of cosines, we get \(\cos(γ) = -0.8570236576028272\)
Step 6 :Taking the arccos of \(\cos(γ)\), we find that γ = 149 degrees.
Step 7 :Final Answer: The angle between the two forces is \(\boxed{149}\) degrees.