To find the resultant and the equilibrant using trigonometry, we need to break down the given vectors into their horizontal and vertical components.
First, let's find the horizontal and vertical components of the first vector, 330.0 newtons @ 125 degrees.
Horizontal component: 330.0 newtons * cos(125 degrees) = -115.9 newtons
Vertical component: 330.0 newtons * sin(125 degrees) = 277.4 newtons
Now, let's find the horizontal and vertical components of the second vector, 250.0 newtons @ 60.0 degrees.
Horizontal component: 250.0 newtons * cos(60 degrees) = 125.0 newtons
Vertical component: 250.0 newtons * sin(60 degrees) = 216.5 newtons
Next, let's add up the horizontal components and vertical components separately to find the components of the resultant vector:
Horizontal component of the resultant = -115.9 newtons + 125.0 newtons = 9.1 newtons
Vertical component of the resultant = 277.4 newtons + 216.5 newtons = 493.9 newtons
Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
Resultant = sqrt((9.1 newtons)^2 + (493.9 newtons)^2)
Resultant = sqrt(82.81 newtons^2 + 243942.21 newtons^2)
Resultant = sqrt(244025.02 newtons^2)
Resultant ≈ 493.97 newtons
To find the direction of the resultant vector, we can use the inverse tangent function:
Direction = atan(493.9 newtons / 9.1 newtons)
Direction ≈ 89.2 degrees
Therefore, the resultant vector is approximately 493.97 newtons @ 89.2 degrees.
To find the equilibrant vector, we need to find the negative of the resultant vector. The magnitude of the equilibrant vector will be the same as the magnitude of the resultant vector, but the direction will be opposite.
Equilibrant = 493.97 newtons @ (89.2 degrees + 180 degrees)
Equilibrant ≈ 493.97 newtons @ 269.2 degrees