# Component method vector problem

Use the component method to find the resultant(direction and magnitude) of the three forces shown.

Could someone please verify my answers or tell me where I went wrong.

Ax = 500 Cos 30 = -433N
Ay = 500 Sin 30 = -250N
Bx=-250 N
By= 0
Cx=200 Cos 20 = 187.9N
Cy= 200 Sin 20 = 68.4N

R = (-433-250+187.9)I + (-250 + 0 + 68.4)j
= (-495.1, -181.6)
R = sqrt(-495.1^2 + -181.6^2)
= 527N

Tan Theta = 318.4 / 370.9
Theta = 20.1 deg.

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Redbelly98
Staff Emeritus
Homework Helper

Use the component method to find the resultant(direction and magnitude) of the three forces shown.

Could someone please verify my answers or tell me where I went wrong.

Ax = 500 Cos 30 = -433N
Ay = 500 Sin 30 = -250N
Bx=-250 N
By= 0
Cx=200 Cos 20 = 187.9N
Cy= 200 Sin 20 = 68.4N

R = (-433-250+187.9)I + (-250 + 0 + 68.4)j
= (-495.1, -181.6)
R = sqrt(-495.1^2 + -181.6^2)
= 527N
That seems right.

Tan Theta = 318.4 / 370.9
Theta = 20.1 deg.
Looks like the "318" and "370" are typos, and that you actually (and correctly) used 181.6/495.1 instead.

You'll also need to specify which half-axis that angle is measured from (+x, +y, -x, or -y), and whether the angle is above/below/right/left of that half-axis.

If you don't specify that, people normally assume it's from the +x axis, in the counterclockwise direction.