# In a straight trapezoid, acute angle = 60 degrees large side and large base = 20cm each Find the smallest base

August 29, 2021 | education

| From the vertex C of the trapezoid, we lower the height CH, perpendicular to AD.

Consider a right-angled triangle СНD, in which the angle Н = 90, the angle Д = 60, then the angle С = 180 – 90 – 60 = 30. The leg СН lies opposite the angle 300, and therefore is equal to half the length of СD.

НD = СD / 2 = 20/2 = 10 cm.

Then the length of the segment АН = АD – НD = 20 – 10 = 10 cm.

The quadrilateral ABCН is rectangular, since all angles are 90, then BC = AH = 10 cm.

Answer: The smaller base is 10 cm.

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