If an object is pushed at an angle of 61 degrees with a force of 182 N, what is the component force in the vertical direction?

You don't say in respect to which direction the angle is measured!!

 

If we assume it is 61° to the horizontal then the component of force in the vertical direction is 182*sin(61°) N

 

If it is 61° to the vertical then the compponent of force in the vertical direction is 182*cos(61°) N