# Is it possible to solve for the unknown sides and angles in the top triangle? $K$ stands for known angle in the picture.

I have two triangles, I am given two angles of the bottom triangle, and the distance between them. With that I can figure out the rest of the information about the bottom triangle, and one of the angles of the top triangle. I am also given the length of one side of the top triangle. I need to find the rest of the angles and sides of the top triangle. Is it even possible to solve for this with the information available, or am I just wasting my time?

• A word of advise, if you want to get real help, don't just put "Known" or "K" on all sides and angles. Better name them with different letters and state in parentheses whether it is known or not. And secondly no, it is not solvable, as the top side could have whichever angle and length you'd want without changing the the values of known sides and angles. – John Mayne Sep 24 '16 at 18:45
• With an angle and a side known, the top triangle is underdetermined. Is there no additional informatiopn? For example, in the sketch the top triangle seems to be isosceles ... – Hagen von Eitzen Sep 24 '16 at 18:49
• It is not possible. You can clearly make the top left angle larger and the top right angle smaller and adjust the sides to make a new triangle that still satisfies the given/known values. – Simply Beautiful Art Sep 24 '16 at 18:50

## 1 Answer

This is not possible. Say the top segment has length $d$, and label the $4$ points in your diagram $A$, $B$, $C$, and $D$ (clockwise from top left). Call the center $E$.

There are infinitely many pairs of points, one on $AD$ and one on $BC$, such that the distance between them is $d$. You can imagine this as turning the top segment at different angles.