Question 1205848
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Refer to the diagram that tutor Edwin has posted.


Triangle ABE is a 30-60-90 triangle, so AB = 4 leads to AE = 2.
The short leg (AE) is half as long as the hypotenuse (AB) for 30-60-90 triangles.
The long leg of 30-60-90 triangles is {{{sqrt(3)}}} times that of the short leg.
Therefore we can state {{{EB = AE*sqrt(3) = 2*sqrt(3)}}}


Triangle DFC is a 45-45-90 triangle.
The hypotenuse DC is {{{sqrt(2)}}} times that of the leg length 
{{{DC = DF*sqrt(2)}}}
{{{DC = 2*sqrt(3)*sqrt(2)}}}
{{{DC = 2*sqrt(3*2)}}}
{{{DC = 2*sqrt(6)}}}
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