Solving gradients of right angle triangle

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The discussion focuses on understanding the calculation of gradients in a right-angle triangle, specifically how m3 is derived. It highlights that without specific lengths for the triangle's sides, m3 can vary while still maintaining the triangle's properties. The user seeks clarification on how u1 is calculated, assuming it involves the gradient of a green line. The equation presented suggests a relationship between m3, u1, and other variables, but the user is uncertain about the derivation of m3. The conversation emphasizes the need for clear definitions and calculations in solving gradient problems in geometry.
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Please take a look at attached diagram displaying gradients of each line, please explain how m3 is obtained.
Gradient Problem.jpg
 
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No. If you don't specify how long the arms of the short sides of the right triangle need to be, then you can make m3 be whatever you want, and you'll still have a right-triangle with 1/x and -x as the gradient of two of the sides.
 
True I think I might of head down the wrong path I am trying to solve the following problem in the diagram below. I am unsure how u1 is obtained. I assume that the gradient of the green line is used to solve as shown below

m3 = (hz+delta_hz)/(u1)
therefore
u1 = (hz+delta_hz)/m3
where
m3 = 1/k3+k3

If this is the case then how has m3 = 1/k3 + k3 been calculated?
Otherwise can you please explain how u1 has been obtained?
Geometric Problem.jpg
 

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