1. Understand the Problem

You have two forces:

* Force 1 (F1): 30 N at 34 degrees (presumably from the horizontal axis)

* Force 2 (F2): 30 N at 76 degrees (presumably from the horizontal axis)

2. Resolve Forces into Components

Each force can be broken down into horizontal (x) and vertical (y) components:

* F1x = F1 * cos(34°) = 30 N * cos(34°) = 24.87 N

* F1y = F1 * sin(34°) = 30 N * sin(34°) = 16.73 N

* F2x = F2 * cos(76°) = 30 N * cos(76°) = 7.21 N

* F2y = F2 * sin(76°) = 30 N * sin(76°) = 28.98 N

3. Calculate Resultant Components

Add the x and y components separately:

* Rx = F1x + F2x = 24.87 N + 7.21 N = 32.08 N

* Ry = F1y + F2y = 16.73 N + 28.98 N = 45.71 N

4. Find the Magnitude of the Resultant Force

Use the Pythagorean theorem:

* R = √(Rx² + Ry²) = √(32.08² + 45.71²) = 56.09 N

5. Determine the Direction of the Resultant Force

Use the arctangent function (tan⁻¹):

* θ = tan⁻¹(Ry / Rx) = tan⁻¹(45.71 / 32.08) = 54.97°

Answer:

The resultant force has a magnitude of 56.09 N and is directed at an angle of 54.97° from the horizontal axis.