The midline of a rectangular trapezoid is 6 cm. The acute angle is 30. Point M is located at a distance of 4 cm

| May 7, 2021 | education

The midline of a rectangular trapezoid is 6 cm. The acute angle is 30. Point M is located at a distance of 4 cm from the plane of the trapezoid, and is at an equal distance from its sides. Find the distance from point M to the sides of the trapezoid.

Since point M is equidistant from the sides of the trapezoid, it is projected to the center of the circle inscribed in the trapezoid.

Since a circle can be inscribed in a trapezoid, then AD + BC = AB + CD.

AB + CD = 2 * KM = 2 * 6 = 12 cm.

AD + BC = 12 cm

Angle A = 30, then AD = 2 * EH = 2 * BC = 4 * R.

4 * R + 2 * R = 12.

R = 2 cm.

In a right-angled triangle MOE, OE = R = 2 cm, then, by the Pythagorean theorem, ME ^ 2 = OE ^ 2 + OM ^ 2 = 4 + 16 = 20.

ОЕ = 2 * √5 cm.

Answer: From point M about the sides of the trapezoid 2 * √5 cm.



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