Math CentralQuandaries & Queries


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.


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


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