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 Question from Peter, a student: Ok, is it possible to find the height and base of a right triangle when all the information you are given is the length of the hypotenuse? I also know that the angle between side b and the hypotenuse is 45 degrees. please help.

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

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.