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In the diagram, triangle ABE, triangle BCE and triangle CDE are right-angled, with Angle AEB= Angle BEC= Angle CED=60 degrees, and AE=24. Find the length of CE.

 

Guest Aug 12, 2018
 #1
avatar+7447 
+1

In the diagram, triangle ABE, triangle BCE and triangle CDE are right-angled, with Angle AEB= Angle BEC= Angle CED=60 degrees, and AE=24. Find the length of CE.

 

\(\overline{BE}=\overline{AE}\cdot cos\ 60\ degrees\\ \overline{BE}=24\cdot cos\ 60\ degrees=24\cdot 0.5=12\\ \overline{CE}=\overline{BE}\cdot cos\ 60\ degrees\\ \overline{CE}=12\cdot cos\ 60\ degrees=12\cdot 0.5=6\\ \)

\(\overline{CE}=6 \)

 

until the end

[\(\overline{DE}=\overline{CE}\cdot cos\ 60\ degrees\\ \overline{DE}=6\cdot cos\ 60\ degrees=6\cdot 0.5=3\\ \color{blue}\overline{DE}=3\)

 

laugh  !

asinus  Aug 12, 2018
edited by asinus  Aug 12, 2018
 #2
avatar+88775 
+2

ΔABE  ~ Δ BEC   which implies that

 

AB/ BE = BE / EC

 

And  ΔABE   is a 30 - 60 - 90 right triangle....AE  = 24  and BE  = 1/2 of this  = 12

 

So

 

24 / 12  = 12 / EC

 

12 /6  = 12 / EC

 

EC   =  CE  = 6

 

 

cool cool cool

CPhill  Aug 13, 2018

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