In a rectangular trapezoid, the larger side is 6 cm, forming an angle of 120 with the smaller base

| August 6, 2021 | education

In a rectangular trapezoid, the larger side is 6 cm, forming an angle of 120 with the smaller base. What should be the bases of the trapezoid so that a circle can be inscribed into it.

Let’s draw the height of the CH trapezoid. In a right-angled triangle СDН, the angle DСН = (ВСD – ВСН) = (120 – 90) = 30.

The leg DН in a right-angled triangle DСН lies opposite the angle 30, then DН = СD / 3 = 6/2 = 3 cm.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 36 – 9 = 27.

CH = AB = √27 = 3 * √3 cm.

Since a circle is inscribed in the trapezoid, then (AB + CD) = (BC + AD).

(3 * √3 + 6) = (BC + AH + DH) = (2 * BC + 3).

2 * BC = (3 * √3 + 6 – 3).

BC = (3 * √3 + 3) / 2.

AD = BC + DH = (3 * √3 + 3) / 2) + 3 = (3 * √3 + 9) / 2 cm.

Answer: The lengths of the bases should be equal to (3 * √3 + 3) / 2 and (3 * √3 + 9) / 2 cm.



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