# The bases of the trapezoid are 30 and 15, and the sides are 9 and 12. Find the angle that the straight

July 29, 2021 | education

| **The bases of the trapezoid are 30 and 15, and the sides are 9 and 12. Find the angle that the straight lines containing the sides make.**

Through point B we draw a straight line BH parallel to the lateral side CD.

Then the sought angle AED is equal to the angle ABH as the corresponding angles at the intersection of parallel straight lines BC and AD secant AE.

The quadrangle ВСDН is a parallelogram, since its opposite sides are equal, then ВН = СD = 12 cm, DH = ВС = 15 cm, АН = АD– DH = 30 – 15 = 15 cm.

In triangle ABH, the lengths of the sides are 9 cm, 12 cm, 15 cm.

9 ^ 2 + 12 ^ 2 = 81 + 144 = 225.

152 = 225.

Since the Pythagorean theorem is fulfilled, the angle ABH = AED = 90.

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