Answer:
AE = 22.86
Step-by-step explanation:
In triangle CDE
cos 30° = CD/CE
[tex] \frac{\sqrt 3}{2} = \frac {7\sqrt 3}{CE}[/tex]
[tex]CE= {7\sqrt 3}\times \frac{2}{\sqrt 3} [/tex]
[tex]CE= 14 [/tex]
In triangle BCE
sin 45° = CE/BE
[tex] \frac{1}{\sqrt 2}= \frac{14}{BE}[/tex]
[tex]BE= 14\sqrt 2[/tex]
In triangle ABE
sin 60° = BE/AE
[tex] \frac{\sqrt 3}{2}= \frac{14\sqrt 2}{AE}[/tex]
[tex]AE= 14\sqrt 2\times\frac{2}{\sqrt 3} [/tex]
[tex]AE= \frac{28\sqrt 2}{\sqrt 3} [/tex]
[tex]AE= \frac{28\sqrt 6}{ 3} [/tex]
[tex]AE= \frac{68.5857128}{ 3} [/tex]
AE = 22.8619043
AE = 22.86
