[net.puzzle] Geometry Puzzle SOLUTION

matt@oddjob.UChicago.UUCP (Matt Crawford) (07/09/84)

Given information:
	BAC = 40,  ABE = ADE = 10,  AB = AD,  B != D.

(1) Exterior angle thm ==> AEB = BAC - ABE = 40 - 10 = 30

(2) sin AEB   sin ABE
    ------- = -------    (law of sines)
      AB        AE

              sin ADE
            = -------    (given ABE=ADE)
                AE

              sin AED
            = -------    (law of sines)
                AD

              sin AED
            = -------    (given AD=AB)
                AB

    Therefore  sin AEB = sin AED.  But  B != D  ==>  AEB != AED,
    so  AED = 180 - AEB = 180 - 30 = 150

(3) DAE = 180 - ADE - AED = 180 - 10 - 150 = 20.

___________________________________________________________
Matt		University	ARPA: crawford@anl-mcs.arpa
Crawford	of Chicago	UUCP: ihnp4!oddjob!matt