This is a really easy arm to solve for.

First you need to label each joint. J0 is the rotating base joint, T1 is the vertical translating joint, and T2 is the horizontal translating joint.

You have three components to solve for: x,y, z

And you have three degrees of freedom:

J0 -> angle

T1 -> height

T2 -> length

So you need to write an equation that uses all 6 variables.

z is easy, since only one joint controls it:

z=T1

Then to get x and y, use highschool geometry + trig, and the top view of your image to solve for it. For example, if the are is at theta and the length is T2, what is x and y?

Solve this and let me know if you are still having trouble or want me to verify it.