# Ratio of Triangle Sides. Calculate Length of Unknown Side using limited data.

In looking at the Triangle below, is there a ratio between sides f and g that would allow me to calculate side j based on i. Or another way to calculate side j?

Triangle Problem

Ok,Sorry.. my problem is different than my original image.. Applying Pythagorean,.. twice would solve my first image. Thank you. What about a solution for the following different problem?

Sides j and k are both always known actually based on distance sensors, but I need a calculation to know what the ratio(?..) between the sides will be when I'm lined up perpendicular as shown in the next image. It's 4am and I'm working on Robot navigation problem. Brain dead.. I do not know distance between the two points labeled "fixed points". They can vary during setup and I cannot automatically measure between them to change my program.

Updated Problem Image

• Two applications of the Pythagoras Theorem will get you $j$ in terms of $f$, $g$, and $i$. – Gerry Myerson Jul 30 '17 at 7:09
• There aren't too many unknowns in this problem. You have everything except j and the height of the triangle. If you can't find one unknown yet, try finding the other first! (If you wanted, trying to find angles would also lead to a solution. :) ) – Alex Meiburg Jul 30 '17 at 7:13
• Thank you. That would have worked, but my problem is actually different than I originally posted. I've edited the original post. – Gremlin Jul 30 '17 at 8:19
• In the new diagram, I'm not sure there's enough information to get the unknown length. – Gerry Myerson Jul 30 '17 at 8:47
• I'm curious regarding how your robot navigates. Is the distance to the two fixed points the only thing it knows at any given time? No info on it's heading, distance traveled or similar? – Jens Jul 31 '17 at 16:33