To find the angle that the resultant makes with the 175-pound force, we can use the concept of vector addition. The resultant of two vectors can be found by adding them together using the parallelogram law of vector addition.
First, let's resolve both forces into their x and y components. We'll use trigonometry to do this.
The 175-pound force can be resolved as follows:
Fx1 = 175 * cos(0°)
Fy1 = 175 * sin(0°)
The 230-pound force can be resolved as follows:
Fx2 = 230 * cos(42°)
Fy2 = 230 * sin(42°)
Next, we'll add the x and y components of both forces to find the resultant components:
Rx = Fx1 + Fx2
Ry = Fy1 + Fy2
Now, we can calculate the magnitude of the resultant force:
R = sqrt(Rx^2 + Ry^2)
Finally, we can find the angle that the resultant makes with the 175-pound force using trigonometry:
θ = arctan(Ry / Rx)
By plugging in the calculated values, we can solve for θ.