  The first main results of this note establish forms of the hyperbolic laws of
cosines and sines for certain classes of quadrilaterals and pentagons in the
hyperbolic plane, having at least one ideal vertex and right angles at
non-ideal vertices, in which the length of a horocyclic cross-section at an
ideal vertex plays the role filled by the dihedral angle in the usual versions
of these laws. The final main result bounds the transversal length of a
truncated tetrahedron in three-dimensional hyperbolic space, meaning the
distance from a designated internal edge to its opposite, in terms of the
tetrahedron's entire collection of internal edge lengths. All main results are
established using the unifying perspective of the hyperboloid model and
Lorentzian geometry. A thorough introduction to this perspective is provided,
with references as appropriate.
