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

bystudin | 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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