The large angle of a rectangular trapezoid is 136. Find the length of the shorter side of the trapezoid

| May 11, 2021 | education

The large angle of a rectangular trapezoid is 136. Find the length of the shorter side of the trapezoid if one of its bases is 6 more than the other.

Let’s draw the height of CH from the top of the obtuse angle, then the triangle CDH is rectangular.

Determine the angles of the triangle СDН. Angle НСD = ВСD – ВСН = 136 – 90 = 46, then the angle СDН = 180 – 90 – 46 = 44.

By condition, the difference in the lengths of the bases of the trapezoid is 6 cm. AD – BC = 6 cm.

Since the trapezoid is rectangular, and CH is height, then the quadrangle ABCH is a rectangle, then BC = AH, and DH = AD – AH = AD – BC = 6 cm, and BA = CH.

Then, in a right-angled triangle, we determine the length of CH.

tg44 = CH / DH.

CH = DH * tg44 = 6 * tg44 cm.

Answer: The length of the smaller side is 6 * tg440.



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