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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-> 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):
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
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
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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