Thread: How much is alpha?

Hello !

We have a square - find alpha ?

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

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 !

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".

Originally Posted by Archie Meade

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 !