Calculating the range of value for which cables will remain taut.

Determine the range of values of «P» for which both cables remain taut. Please see the attachment for a drawing of the solution.

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...ate Tac:
Tac=(424,3-Tbc*cos30°)/cos30°
After, I take «Tac» into the first equation, and I found «Tbc»:
424,3+Tbc*0,5-0,5*((424,3-Tbc*0,866)/0,866)=P
Tbc=P-179,3
From this answer, I found Tac:
424,3+(P-179,3)*0,5-Tac*0,5=P
Tac=669,2-P

<br>Tbc = P - 179.3
<br>Tac = 669.2 - P
<br>
<br>I'm not quite sure what that force was pulling down and to the ...