I have a similar triangles question which I am stuck on. What is known is the angle $\theta$ and the length $y$ (values don't really matter). While the lengths $\alpha$, $\beta$, $t$, $\gamma$, $\delta$ and $x$ are all unknowns. Through trigonometry, I was able to obtain values for $\gamma$+$\delta$ and $t$+$\beta$. What I want to know is if there is a way to determine the value of $t$ or are there simply too many unknowns to do so. Any help is appreciated. Feel free to edit my question for clarity. Sorry for my hand writing but $\gamma$ is the length at the top of the triangle, $y$ is the longest length
Consider that, with fixed $\,y, \theta\,$ and moving the point defined by $\,\alpha\,$ along the hypotenuse:
for $\,\alpha \to 0\,$: $\;t\to y \cos(\theta)\,$
for $\,\alpha \to y\,$: $\;t \to 0\,$
There is simply not enough information to solve the figure for $\,t\,$, since each $\,0 \le \alpha \le y\,$ would give a different $\,t = (y - \alpha) \cos(\theta)\,$.