In trapezoid ABCD, base BC is perpendicular to side AB, angle D is 60, diagonal AC is perpendicular

| February 10, 2021 | education

In trapezoid ABCD, base BC is perpendicular to side AB, angle D is 60, diagonal AC is perpendicular to side CD equal to 8cm. Find the base length BC.

From the top of the trapezoid, we lower the height CH.

In the formed right-angled triangle СНD, angle D = 60, angle H = 90, then angle C = 180 – 90 – 60 = 30.

The DН leg lies opposite an angle of 30, and therefore is equal to half the length of the СD hypotenuse.

DН = СD / 2 = 8/2 = 4 cm.

Consider a right-angled triangle AСD, in which angle D = 60, angle C = 90, then angle A = 180 – 90-60 = 30.

The СD leg lies opposite the angle A equal to 300, therefore it is equal to half the length of the hypotenuse of blood pressure. Then AD = 2 * СD = 2 * 8 = 16 cm.

Segment AH = ADL – DН = 16 – 4 = 12 cm.

Since ABCH is a rectangle, BC = AH = 12 cm.

Answer: Base length BC = 12 cm.



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