The bases of a rectangular trapezoid are equal to a and b, one of the criminals is equal to a.
| September 16, 2021 | education
The bases of a rectangular trapezoid are equal to a and b, one of the criminals is equal to a. Find: the smaller side of the trapezoid if a = 10 cm, b = 15 cm, a = 45.
From the top of the obtuse angle C of the trapezoid, we lower the height of CH to the base of AD.
Consider a right-angled triangle СНD, in which the angle Н is straight, and the angle НDС, by condition, is 45, then the angle DСН = 180 – 90 – 45 = 45, therefore the triangle СНD is equilateral and СН = DH.
Since the trapezoid is rectangular, and CH is perpendicular to AD, then the quadrilateral ABCH is a rectangle, then CB = AH = 10 cm, and DH = CH = AD – AH = 15 – 10 = 5 cm.Therefore, AB = CH = 5 cm …
Answer: The smaller side is 5 cm.
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