An equilateral triangle ABC shares a common side BC with a square BCDE, as pictured. What is the number of degrees in angle DAE (not pictured)?

anomy
Aug 11, 2018

#1**+1 **

For convenience sake...let the side of the square = 1

Then the height of the equilateral triangle = √3/2

Position D at (0,0)

Then A will have the coordinates ( 1/2, 1 + √3/2)

And we can find 1/2 of the measure of angle DAE as

arctan [ (1/2) / ( 1 +√3/2 ) ] = 15°

So...DAE will be twice this = 30°

CPhill
Aug 11, 2018

#2**+1 **

Actually....this could be done more simply

Draw AD....now....we have ΔACD with angle ACD = 150°

And since CD = CA, then angle CAD and And ADC are equal

So angle CAD = [180 -150 ] / 2 = 30/2 = 15°

And if we draw, AE, by the same process, in Δ ABE, angle EAB = 15°

So CAB = 60° = angle CAD + angle DAE + angle EAB

60 = 15 + angle DAE + 15

60 = 30 + angle DAE

30° = angle DAE

CPhill
Aug 13, 2018