Step1

Consider the modified diagram for the provided one.

Here in the diagram, the angles alpha, beta and gamma are shown, which is the angle between the 106lb force and x-axis, 102 lb fore with the x axis (negative) and 200 lb force with y axis (negative) respectively. The x and y components of all the forces are also shown in the above diagram.

Step 2

The subsequent step is to determine the angles,

For the angle alpha, consider the right angled triangle AOB and apply the trigonometric ratio for the tangent angle,

Step 3

The x-component of the force having the value 106 lb will be,

Step 4

Further, for the angle beta, consider the right angled triangle DOE and apply the trigonometric ratio for the tangent angle,

Step 5

The x-component of the force having the value 102 lb will be,

Step 6

Finally, for the angle gamma, consider the right angled triangle GOH and apply the trigonometric ratio for the tangent angle,

Step 7

The x-component of the force having the value 200 lb will be,