Originally Posted by

**LumusRedfoot** *We are presented with the problem:*

The hyperbolic lines l, m and n defined by:

l={zEH | abs(z-1)=2}

m={zEH | **Re**(z)=2}

n={zEH | abs(z-3)=2rt3}

form a hyperbolic triangle with vertices: A:= m **n **n, B:= l **n** n and C:= l **n** m.

(i) Find the complex numbers which represent A, B and C

(ii) Draw a diagram to scale of the hyperbolic lines l, m and n. Label their points of intersection and their intersections with the real axis with the appopriate letters and complex numbers.

(iii) Two of the interior angles are denoted: x at B and y at C. Give exact expressions for cos(y), sin(y) and cot(x). Calculate the angles x and y to 3dp.

(iv) Let a denote the length of the h-line segment BC and b denote the length of the h-line segment AC. Calculate a and b exactly in terms of natural logarithms and also approximately, to 4dp.

(v) Using the exact answers in (iii) and (iv), verify exactly, for the given hyperbolic triangle, the identity: cos(y)cosh(a)=sinh(a)coth(b)-sin(y)cot(x).

*My apologies if this is in the wrong forum as this is university Geometry, but there was not a university Geometry forum appropriate to put it in. It is not pre-university but it is is Geometry. I'm not seeking full-blown solutions just a little kickme in the right direction. This is my weakest module and I really don't quite understand it. There are no course materials, reading lists etc, and the teaching staff do not accept questions or queries about the work. So I am asking here. Thanks if anyone can give me a few pointers.*

*Lumus*