a 150-N and 80-N force act upon an object. the angle between the two forces is 55 degrees. determine the magnitude and direction by trigonometric calculations.

To determine the magnitude and direction of the resultant force, you can use the trigonometric calculations involving the given forces.

First, let's resolve the forces into their components. The 150-N force can be broken down into its horizontal and vertical components as follows:

F₁x = 150 N * cos(0°) = 150 N
F₁y = 150 N * sin(0°) = 0 N

Similarly, for the 80-N force:

F₂x = 80 N * cos(55°)
F₂y = 80 N * sin(55°)

Now, we can find the components of the resultant force by summing up the individual components:

Fₓ = F₁x + F₂x
Fᵧ = F₁y + F₂y

Substituting the given values:

Fₓ = 150 N + 80 N * cos(55°)
Fᵧ = 0 N + 80 N * sin(55°)

Next, we can calculate the magnitude and direction of the resultant force using these components:

Magnitude (F):
F = √(Fₓ² + Fᵧ²)

Direction (θ):
θ = tan⁻¹(Fᵧ/Fₓ)

Substituting the calculated values:

Magnitude (F):
F = √((150 N + 80 N * cos(55°))² + (80 N * sin(55°))²)

Direction (θ):
θ = tan⁻¹((80 N * sin(55°))/(150 N + 80 N * cos(55°)))

Evaluating these trigonometric calculations will give you the desired results.