Right triangle problem,please check

AI Thread Summary
The discussion revolves around solving a right triangle problem involving segments TN, NK, ST, and SN. The Pythagorean Theorem is applied to find the length of TK, with SN identified as the median of the triangle. Participants suggest marking the unknown side with a variable to create two equations from the two right triangles present. By applying the theorem to both triangles, users can solve for the unknowns effectively. Ultimately, the correct answer is achieved through this method.
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Right triangle problem,please check!

Homework Statement


In the figure,TN=NK, ST=12 and SN=\sqrt{69}.Find the length of TK.
[PLAIN]http://img695.imageshack.us/img695/633/50042657.png


Homework Equations


Pythagorean Theorem


The Attempt at a Solution


Segment SN is the median of the right triangle.Here its not given the other leg how can we find a or b ?
 
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There are two right angled triangles on the picture. They have a common side. Although you do not know the length of it, I would suggest you mark it with some letter. Then, write out Pythagora's Theorem for both of them. You will have two equations for two unknowns.
 


Yes,you are right, thanks a lot.I got the correct answer
 

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