Peter,
So you actually have THREE pieces of information:
 one of the angles is a right angle
 a second angle is 45 degrees
 the length of the hypotenuse.
Generally, for a triangle, three facts can be enough (and two are not).
So one can imagine (sketch with something like Geometer's Sketch Pad) a unique triangle with these properties.
The length you want is determined  but you still need strategies to calculate them.
Some steps:
 can you find the third angle given the other two angles?
 if you know trig, you can now find what you wanted.
 can you see any symmetry in these angles and the rest of the pattern?
 with the symmetry (of the base and the height) can you now use formulae (e.g. Pythagoras) to find the missing sides?
Walter Whiteley
