ABCD – trapezoid, AD parallel to BC, AB perpendicular to AD, angle D = 60 degrees.

| April 17, 2021 | education

ABCD – trapezoid, AD parallel to BC, AB perpendicular to AD, angle D = 60 degrees. Find the base BC if CD = 7cm, AC is perpendicular to CD.

From the top of the obtuse angle, draw the height of the CH.

In a right-angled triangle СDН the angle DСН = 180 – 90 – 60 = 30, then the segment DН is equal to half the length of СD, since it lies opposite the angle 30.DН = 7/2 = 3.5 cm.

Let us determine the length of the CH height by the Pythagorean theorem.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 49 – 12.25 = 36.75.

By condition, the triangle ACD is rectangular, then by the property of the height drawn to the hypotenuse from the vertex of the right angle CH ^ 2 = AH * DH.

36.75 = AH * 3.5.

AH = 36.75 / 3.5 = 10.5 cm.

Since the quadrangle ABCН is a rectangle, then BC = AH = 10.5 cm.

Answer: The length of the BC base is 10.5 cm.



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