It's been a while since I took Geometry, apologies if this is obvious but I couldn't find an answer while searching. I have a right trapezoid:
The sides a, b, and c are known. Can I find the remaining two angles given the information I have?
[Math] Finding the angles in a right trapezoid
geometry
Related Solutions
Ok, here is one approach that works. Since diagonals are equal, and bases are parallel, it is easy to show that top and bottom triangle are similar, using alternate interior and vertical angles theorem. Let's call the diagonal intersection point S and vertices of the trapezoid A,B,C,D with A at bottom left vertex. Now BS is a multiple of DS (say factor k) and AS is a multiple of CS (same factor k) Now use area formula for triangle ½*b*c*sin(enclosed angle) on left and right triangle to show that these areas are equal. You will in both cases arrive at area ½*AS*DS*sin(angle) for left and right triangle of the trapezoid. KNowing that these triangles are congruent, and top and bottom triangles are similar, I think you can finish the proof
Clearly the figure is a trapezoid because you can construct an infinite number of quadralaterals consistent with the given constraints so long as the vertical height $h$ obeys $0 < h \leq 9$ inches. Only one of those infinite number of figures is a square.
I would email the above statement to the teacher... but that's up to you.
As for the "politics" or "pedagogy" of drawing a square, but giving conditions that admit non-square quadralaterals... well, I'd take this as a learning opportunity. The solution teaches the students that of course any single drawing must be an example member of a solution set, but need not be every example of that set. In this case: a square is just a special case of a trapezoid.
The solution goes further and reveals that the vertexes (apparently) lie on a semi-circle... ("obvious" to a student). A good followup or "part b" question would be to prove this is the case.
Best Answer
from pedal triangle angle = $\pi/2+\arctan{\frac{c-b}{a}}$
Sorry for my bad English