In an equilateral trapezoid, the diagonal is 18 cm and forms an angle of 60 degrees with the base
| February 15, 2021 | education
In an equilateral trapezoid, the diagonal is 18 cm and forms an angle of 60 degrees with the base. Find the bases of the trapezoid if their difference is 10 cm.
From the tops of the obtuse angles of the trapezoid, we draw the heights of the ВН and СK. Since the trapezoid of AВСD is isosceles, the heights of the ВН and СK are cut off on a larger base equal segments. AH = DK.
By condition, AD – BC = 10 cm, then (AH + DK) = 10 cm, and AH = DK = 10/2 = 5 cm.
In a right-angled triangle ACН, the angle ACН = 180 – 90 – 60 = 30, then the leg AK lies against the angle 30, then AK = AC / 2 = 18/2 = 9 cm.
Segment НK = AK – AН = 9 – 5 = 4 cm.Then BC = 4 cm, AD = AK + DK = 9 + 5 = 14 cm.
Answer: The bases of the trapezoid are 4 cm and 14 cm.
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