# Thread: How much is alpha?

1. ## How much is alpha?

Hello !

We have a square - find alpha ?

2. ## Re: How much is alpha?

There is not enough information to answer.
There must be more given. What else do you know?

3. ## Re: How much is alpha?

Originally Posted by Plato
There is not enough information to answer.
There must be more given. What else do you know?
Sorry !

This is a square !

4. ## Re: How much is alpha?

Rotate triangle AEB about B, until A rests on C.
Label the new position of "E" as "G".
Draw a line from E to G.
Angle EBG is 90 degrees.
Angles BEG and BGE are 45 degrees.
Use Pythagoras' Theorem to calculate |EG|

Triangle ECG now has all 3 sides (if you let |AE|=1, |EB|=2, |EC|=3)
and you rearrange the law of cosines to calculate "alpha-45" degrees
and therefore "alpha".

5. ## Re: How much is alpha?

Rotate triangle AEB about B, until A rests on C.
Label the new position of "E" as "G".
Draw a line from E to G.
Angle EBG is 90 degrees.
Angles BEG and BGE are 45 degrees.
Use Pythagoras' Theorem to calculate |EG|

Triangle ECG now has all 3 sides (if you let |AE|=1, |EB|=2, |EC|=3)
and you rearrange the law of cosines to calculate "alpha-45" degrees
and therefore "alpha".
Thank you !

You're a genius ! God blesse you !