# Find the side AB of the trapezoid ABCD if the angles ABC and BCD are 30 ° and 120 ° respectively, and CD = 25

May 31, 2020 | Education

| Find the segments as shown in the figure.

DE = AF, because these are the heights of the trapezoid.

∠DCE = 180 ° -∠BCD = 180 ° -120 ° = 60 ° (since these are adjacent angles).

sin (∠DCE) = ED / CD (by definition)

sin60 ° = ED / CD

√3 / 2 = ED / 25

ED = 25√3 / 2

sin (∠ABF) = AF / AB (by definition)

sin30 ° = ED / AB

AB = ED / sin30 °

AB = ED / (1/2)

AB = 2ED = 2 * 25√3 / 2 = 25√3

Answer: AB = 25√3

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