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.
 
+0  
 
0
443
2
avatar+45 

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)?

 Aug 11, 2018
 #1
avatar+100519 
+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°

 

 

cool cool cool

 Aug 11, 2018
 #2
avatar+100519 
+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

 

 

cool cool cool

 Aug 13, 2018

8 Online Users

avatar