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M2 Conical Pendulum Question - Need Help

Hi all,

I'm having problems with a conical pendulum question, in particular because there are two unknowns. I'd love to be able to provide a diagram, but I'm unable to so I'm hoping most people are able to picture a typical conical pendulum scenario in their heads with the wording of the question:

A conical pendulum consists of a light inextensible string AB of length 50cm fixed at A and carrying a bob of mass 2kg at B. The bob describes a horizontal circle about the vertical through A with a constant angular speed of 5 rad/s. Find the tension in the string

Resolving vertically and horizontally:

T\cos \theta \ = mg

T\sin \theta \ = mrw^2

Dividing equation 2 by equation 1, eliminates R and m leaves:

\tan \theta \ = \frac{rw^2}{g}

Problem is I'm left with two unknowns, theta and the radius r, and I'm stumped.

I know based on experience because the hypotenuse is 50cm, both vertical length and r must be 40cm and 30cm respectively, but I can't prove that and if the hypotenuse were less straight forward, I wouldn't know how to obtain the radius.

(BTW this question comes from exercise 13C, question 7 in understanding mechanics by A.J Sadler/D.W.S Thorning if anyone has it)