The body is in balance under the influence of three forces. One force (6 N) acts to the east, the other (3N)

The body is in balance under the influence of three forces. One force (6 N) acts to the east, the other (3N) at an angle of 60 ° – to the northeast. Determine the modulus and application of the third force.

Given:
F1 = 6 Newton, modulus of the first force directed to the east;
F2 = 3 Newtons – the modulus of the second force directed to the north-east.
It is required to determine the modulus and direction of the third force F3.
According to the condition of the problem, the body is in equilibrium. This means that the sum of all the forces acting on the body is equal to 0. Then, it turns out, the force F3 must be directed to the southwest with some angle a for equality to hold. Let us expand the forces along the axis to the east and along the axis to the north. Then:
F3 (east) = F1 + F2 * cos (60) = 6 + 3 * 0.5 = 6 + 1.5 = 7.5
F3 (north) = F2 * sin (60) = 3 * 0.87 = 2.61
F3 = (F3 (east) ^ 2 + F3 (north) ^ 2) ^ 0.5 = (7.5 ^ 2 + 2.6 ^ 2) ^ 0.5 = (56.2 + 6.8) ^ 0, 5 = 63 ^ 0.5 = 7.9 Newton.
Then the direction of force will be:
cos (a) = F3 (east) / F3 = 7.5 / 7.9 = 0.94. Hence a = 19 degrees.
Answer: the modulus of the third force is 7.9 Newtons, it is directed to the southwest at an angle of 19 degrees to the horizontal.