If five forces act towards the same point on a body at angles of 60, 120, 180, 240 and 270 degrees and their respective magnitudes are 60N, 40N, 30N, 25N and 20N. Determine whether this system of forces is in equilibrium; find the resultant.

You have to add them as vectors. Not knowing from where the angles are measured and in what direction, I can't help.

To determine whether the system of forces is in equilibrium, we need to check if the sum of all the forces acting on the body is equal to zero. If the sum is zero, then the forces balance each other out and the system is in equilibrium. If the sum is not zero, then the system is not in equilibrium.

To find the resultant force, we need to find the vector sum of all the individual forces. The resultant force will be a single force that represents the combined effect of all the individual forces.

First, let's resolve each force into its horizontal and vertical components using the given angles:

For the force with a magnitude of 60N at an angle of 60 degrees:
Horizontal component = 60N * cos(60) = 30N
Vertical component = 60N * sin(60) = 51.96N

For the force with a magnitude of 40N at an angle of 120 degrees:
Horizontal component = 40N * cos(120) = -20N
Vertical component = 40N * sin(120) = 34.64N

For the force with a magnitude of 30N at an angle of 180 degrees:
Horizontal component = 30N * cos(180) = -30N
Vertical component = 30N * sin(180) = 0N

For the force with a magnitude of 25N at an angle of 240 degrees:
Horizontal component = 25N * cos(240) = -12.5N
Vertical component = 25N * sin(240) = -21.65N

For the force with a magnitude of 20N at an angle of 270 degrees:
Horizontal component = 20N * cos(270) = 0N
Vertical component = 20N * sin(270) = -20N

Now, let's calculate the sum of the horizontal and vertical components:

Horizontal component: 30N + (-20N) + (-30N) + (-12.5N) + 0N = -32.5N
Vertical component: 51.96N + 34.64N + 0N + (-21.65N) + (-20N) = 44.95N

The sum of the horizontal components is -32.5N, and the sum of the vertical components is 44.95N.

Therefore, the system of forces is not in equilibrium since the sum of the horizontal and vertical components is not equal to zero.

To find the resultant force, we can use the Pythagorean theorem:

Resultant magnitude = sqrt((-32.5N)^2 + (44.95N)^2) = 54.38N

To find the angle of the resultant force, we can use the inverse tangent function:

Resultant angle = arctan(44.95N / -32.5N) = -54.74 degrees

Therefore, the resultant force has a magnitude of 54.38N and an angle of -54.74 degrees.