The road embankment in the upper part is 60 m wide. What is the embankment
| March 13, 2021 | education
The road embankment in the upper part is 60 m wide. What is the embankment width in its lower part if the slope angle is 60 degrees and the embankment height is 12 m?
The road embankment is an isosceles trapezoid. AB = CD.
Let’s build the heights of the HВ and СK. In a right-angled triangle CDK, tg60 = CK / DK.
DC = CK / tg60 = 12 / √3 = 4 * √3 m.
Rectangular triangles ABN and CDK are equal in leg and hypotenuse, then AH = DK = 4 * √3 m.
Quadrangle ВСKН is a rectangle, then НK = BC = 60 m.
Base length АD = АН + НК + DК = 4 * √3 + 60 + 4 * √3 = 60 + 8 * √3 = 8 * (7.5 + √3) m.
Answer: The width of the embankment is 8 * (7.5 + √3) m.
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