SOLUTION: Given ABCD is a trapezoid with BC parallel to AD. If AB = AD = 4, angle A = 60 degrees, and angle C = 45 degrees, determine the value of length DC.

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Question 1205848: Given ABCD is a trapezoid with BC parallel to AD. If AB = AD = 4, angle A = 60 degrees, and angle C = 45 degrees, determine the value of length DC.
Found 3 solutions by Edwin McCravy, AnlytcPhil, math_tutor2020:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
I labeled the trapezoid clockwise instead of counter-clockwise. To make
it labeled counter-clockwise, draw the mirror image of this drawing.



Braw BE and FD perpendicular to AD and BC.













Since angle C is 45o, that tells us that triangle DFC is an
isosceles right triangle. The hyptenuse of an isosceles right triangle is
 times either leg.




Edwin
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

The above solution is correct. So that the labeling 
ABCD will be counter-clockwise, you can draw the mirror 
image of the above solution.

AnlytcPhil aka Edwin

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

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 times that of the short leg.
Therefore we can state

Triangle DFC is a 45-45-90 triangle.
The hypotenuse DC is times that of the leg length





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