Final answer:
To find the resultant force by the triangular method, we need to break down the forces into their horizontal and vertical components using trigonometry. The horizontal and vertical components can be found using the cosine and sine functions. The magnitude of the resultant force can be calculated using the Pythagorean theorem.
Step-by-step explanation:
To find the resultant force by the triangular method, we need to break down the forces into their horizontal and vertical components. This can be done using trigonometry.
Let's first find the horizontal components of the forces:
F₁x = F₁ * cos(30°) = 4N * cos(30°) = 4N * √3/2 = 6.93N
F₂x = F₂ * cos(30°) = 5N * cos(30°) = 5N * √3/2 = 8.66N
Now, let's find the vertical components of the forces:
F₁y = F₁ * sin(30°) = 4N * sin(30°) = 4N * 1/2 = 2N
F₂y = F₂ * sin(30°) = 5N * sin(30°) = 5N * 1/2 = 2.5N
The resultant force in the horizontal direction is the sum of the horizontal components:
Fnetx = F₁x + F₂x = 6.93N + 8.66N = 15.59N
The resultant force in the vertical direction is the sum of the vertical components:
Fnety = F₁y + F₂y = 2N + 2.5N = 4.5N
Using the Pythagorean theorem, we can find the magnitude of the resultant force:
|Fnet| = sqrt(Fnetx² + Fnety²) = sqrt((15.59N)² + (4.5N)²) = sqrt(242.32N² + 20.25N²) = sqrt(262.57N²) = 16.20N
Therefore, the magnitude of the resultant force is 16.20N.