We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
cookie policy and privacy policy.

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