Question 1178041
Let's solve this problem step-by-step.

**1. Resolve Forces into Components**

* **F1 (150N, 030°):**
    * F1x = 150 * cos(30°) = 150 * (√3 / 2) ≈ 129.90 N
    * F1y = 150 * sin(30°) = 150 * (1/2) = 75 N

* **F2 (x N, 120°):**
    * F2x = x * cos(120°) = x * (-1/2) = -x/2 N
    * F2y = x * sin(120°) = x * (√3 / 2) ≈ 0.866x N

* **R (y N, 090°):**
    * Rx = y * cos(90°) = y * 0 = 0 N
    * Ry = y * sin(90°) = y * 1 = y N

**2. Set Up Equations for Resultant Force**

The resultant force is the vector sum of the individual forces:

* Rx = F1x + F2x
* Ry = F1y + F2y

Substitute the component values:

* 0 = 129.90 - x/2
* y = 75 + 0.866x

**3. Solve for x**

From the first equation:

* x/2 = 129.90
* x = 129.90 * 2
* x = 259.80 N

**4. Solve for y**

Substitute the value of x into the second equation:

* y = 75 + 0.866 * 259.80
* y = 75 + 224.9928
* y = 299.9928 N

**5. Round to Two Decimal Places**

* x ≈ 259.80 N
* y ≈ 299.99 N

**Therefore:**

* x ≈ 259.80 N
* y ≈ 299.99 N