Hello jegues...and the additional clue is in the question, which you quote:tension should be constant over the smooth pulley.There's only one tension asked for, so it must be the same in both parts of the cable....the tension in ADB.
Now, as to your working:
- You have the angle at wrong. , not .
- Your and equations are OK apart from this (and, of course, you need to put the same tension in both parts of the cable). Then:
- You need to take moments to solve this problem. If you take moments about , you'll get the tension immediately. Then use the and equations to find the reaction at .
Here's the equation:Can you complete it now?