Getting coordinate between two coordinates knowing the distance and latitude

Question

That is my wall:

I know the coordinates of the lower points (left and right). (X1,Y1,Z) and (X2,Y2,Z) where X is the latitude, Y longitude and Z the altitude.

I want to know the another point of the picture. Only I know the altitude Z2 and the distance from the lower left corner. How can I get that coordinate?

Answer 1

If I understand it well, you look for $x,y$ such that distance of $(x,y,z_2)$ from $(x_1,y_1,z)$ is 10. So, use the Pythagorean theorem (also works for 3d): $$(x-x_1)^2 + (y-y_1)^2 + (z_2-z)^2 = 100$$ That's all you can get from these inputs.