Two forces of magnitude 20 newtons and 25 newtons respectively act at a point. If the resultant force is 39 newtons, the angle between the forces has to be nearly?

To find the angle between the two forces, we can use the concept of vector addition. The resultant force is the vector sum of the two forces. Therefore, it can be represented as the diagonal of a parallelogram formed by the two forces.

Let's label the two forces as F1 and F2, with magnitudes of 20 newtons and 25 newtons, respectively. The resultant force is given as 39 newtons.

Using the triangle law of vector addition, the magnitude of the resultant force can be calculated as:

Resultant force = √(F1² + F2² + 2F1F2cosθ)

where θ is the angle between the two forces.

Let's rearrange the formula to find the angle θ:

cosθ = (Resultant force² - F1² - F2²) / (2F1F2)

Now we can substitute the given values into the formula:

cosθ = (39² - 20² - 25²) / (2 * 20 * 25)
cosθ = (1521 - 400 - 625) / 1000
cosθ = 496 / 1000
cosθ = 0.496

To find the angle θ, we can take the inverse cosine (arccos) of 0.496 using a calculator:

θ ≈ arccos(0.496)
θ ≈ 59.28 degrees

Therefore, the angle between the forces is approximately 59.28 degrees.