Statics problem

I'm a math major who's trying to improve some physics, on the topic Statics. Here's the problem:

The weighing bowl is suspended on three threads of equal length l. The points at which the threads are attached to the bowl form an equilateral triangle inscribed in a circle of radius R. Determine the thread tension if a weight P is placed in the middle of a bowl. (Disregard the weight of the bowl.)

My approach is to write an equation: Let's call our tension T, then $$3T+P=0$$ We have three threads thus $$3T$$ and P's direction goes down. But I can't figure out how to use circle or triangle. (We can easily write it's side in terms of radius R.)

Book has the answer: $$T=\displaystyle{\frac{Pl}{3\sqrt{l^{2}-R^{2}}}}$$

• You are missing a key piece of information in the problem description. Are the strings hanging vertically down? Or do they all initiate from the same point in the ceiling, thus hanging at an angle? Or something third? – Steeven Mar 10 at 11:22
• @Steeven , nothing about it in the book. – bheadr 73 Mar 10 at 11:27
• Unfortunately this appears to be a key, missing detail that leads to the answer given. The strings must all be attached to a common point above. When this constraint is given, the answer you cite is correct. – jpf Mar 10 at 13:30

$$P = 3 \frac{\sqrt{l^2-R^2}}{l}T$$