Question 3
Given an acute angled triangle \(T\), show that there is a unique tetrahedron whose faces are all congruent to \(T\) and find the volume of this tetrahedron.
Partial Solution by Billy Smells
Let our acute triangle have side lengths \(a\), \(b\) and \(c\).
We can construct a net for the tetrahedron, as shown below: