Engineering Did I Make a Mistake in Solving for the Load Applied at Point D?

[mingyz0403]

Homework Statement

the 48-lb load can be moved along the line of action shown and applied at a, d, or e. determine the components of the reactions at b and f if the 48-lb load is applied at d

Relevant Equations

3 reaction equation

My answer was correct, however my direction was different from the textbook. I have checked my work a few times ,but not able to find out what I did wrong. Could anyone tell me what I did wrong.

Thank you in advance for your help.

 

[PhanthomJay]

I’m not sure what the textbook method was for the load applied at D. You somehow recognized that member ACF was a 2-force member. Otherwise the x and y components of the pin reactions at C and F would not be trigonometrically related . You should have used tangents instead of sin and cos, but nonetheless your answer is correct. What about the other cases? They may not give the same results.