Nancy and Harry are lifting a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120 newtons(N) at a 60 degree angle with the horizontal while Harry is pulling the statue with a force of 180 newtons at a 40 degree andgle with the horizontal. What is the magnitude of the combined forcd they exert on the statue?

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343 To find the magnitude of the combined force exerted by Nancy and Harry on the stone statue, we need to use vector addition. We can break down each force into its horizontal and vertical components.

First, let's find the horizontal and vertical components of Nancy's force:
- Horizontal component (F_Nx) = force (F_N) * cos(angle (θ_N))
F_Nx = 120 N * cos(60°)
F_Nx ≈ 120 N * 0.5
F_Nx = 60 N

- Vertical component (F_Ny) = force (F_N) * sin(angle (θ_N))
F_Ny = 120 N * sin(60°)
F_Ny ≈ 120 N * 0.87
F_Ny ≈ 104.4 N

Now, let's find the horizontal and vertical components of Harry's force:
- Horizontal component (F_Hx) = force (F_H) * cos(angle (θ_H))
F_Hx = 180 N * cos(40°)
F_Hx ≈ 180 N * 0.77
F_Hx ≈ 138.6 N

- Vertical component (F_Hy) = force (F_H) * sin(angle (θ_H))
F_Hy = 180 N * sin(40°)
F_Hy ≈ 180 N * 0.64
F_Hy ≈ 115.2 N

Next, we add the horizontal components and vertical components separately:
- Combined horizontal force (F_combined_x) = F_Nx + F_Hx
F_combined_x = 60 N + 138.6 N
F_combined_x ≈ 198.6 N

- Combined vertical force (F_combined_y) = F_Ny + F_Hy
F_combined_y = 104.4 N + 115.2 N
F_combined_y ≈ 219.6 N

Finally, we can find the magnitude of the combined force using the Pythagorean theorem:
- Magnitude of the combined force (F_combined) = sqrt((F_combined_x)^2 + (F_combined_y)^2)
F_combined = sqrt((198.6 N)^2 + (219.6 N)^2)
F_combined ≈ sqrt(39432.96 N^2 + 48223.36 N^2)
F_combined ≈ sqrt(87656.32 N^2)
F_combined ≈ 296.07 N

Therefore, the magnitude of the combined force that Nancy and Harry exert on the statue is approximately 296.07 newtons (N).