at what angle must the two forces of 50 newton and 120 newton be acting so as to balanced by a force of 130 newton?

Two forces of 5 newton and 12 newton at what angle these forces added to get 17 newton and 7 newton and 13 newton

To find the angle at which the two forces of 50 newtons and 120 newtons must act in order to be balanced by a force of 130 newtons, we can use the concept of vector addition.

First, let's represent the two forces of 50 newtons and 120 newtons as vectors. We'll call the force of 50 newtons as vector A and the force of 120 newtons as vector B.

Next, we need to construct a triangle using vector A, vector B, and the force of 130 newtons (let's call it vector C) as the sides.

Now, to find the angle between vector A and vector B, we can use the Law of Cosines. The formula is as follows:

c^2 = a^2 + b^2 - 2ab * cos(C)

Here, c represents the magnitude (or length) of vector C, a represents the magnitude of vector A, b represents the magnitude of vector B, and C represents the angle between vectors A and B.

We know the magnitudes of vector A, vector B, and vector C. The magnitude of vector A is 50 newtons, the magnitude of vector B is 120 newtons, and the magnitude of vector C is 130 newtons.

Let's substitute these values into the formula:

130^2 = 50^2 + 120^2 - 2 * 50 * 120 * cos(C)

Simplifying further:

16900 = 2500 + 14400 - 12000 * cos(C)

16900 = 16900 - 12000 * cos(C)

12000 * cos(C) = 0

cos(C) = 0

Now, to find the angle C, we need to take the inverse cosine (cos^-1) of 0. This can be done using a calculator.

cos^-1(0) = 90 degrees

Therefore, the two forces of 50 newtons and 120 newtons must act at a right angle (90 degrees) in order to be balanced by a force of 130 newtons.