the angle between two forces of 32 AND (neutrons) and 47 N is 36 degrees. Find the magnitude of the resultant force

To find the magnitude of the resultant force, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their magnitudes and the cosine of the angle between them.

In this case, we have two forces: 32 N and 47 N, and the angle between them is 36 degrees. Let's call the magnitude of the resultant force "R".

Using the law of cosines, we can write the equation as follows:

R^2 = (32^2) + (47^2) - 2(32)(47)cos(36)

Now we can calculate the magnitude of the resultant force:

R^2 = 1024 + 2209 - 2(32)(47)cos(36)
R^2 = 1024 + 2209 - 2992cos(36)

To find R, we take the square root of the right-hand side:

R = √(1024 + 2209 - 2992cos(36))

Now we can use a calculator to evaluate the expression:

R ≈ √(1024 + 2209 - 2992 * 0.809016994) ≈ √(1024 + 2209 - 2417.585) ≈ √(816.415) ≈ 28.57 N

Therefore, the magnitude of the resultant force is approximately 28.57 N.