The lateral side CD of the isosceles trapezoid ABCD is 24, the angle ADC = 60 degrees, the height CH
| June 24, 2021 | education
The lateral side CD of the isosceles trapezoid ABCD is 24, the angle ADC = 60 degrees, the height CH is drawn in the trapezoid. Find the length of the line segment DH.
Since the trapezoid is isosceles, AB = CD = 24 cm.
CH is the height of the trapezoid, then the triangle CDH is rectangular, in which the angle is НDC = АDC = 60, then the angle is DСН = (90 – НDC) = (90 – 60) = 30.
The DH leg lies opposite an angle of 30, then its length is equal to half the length of the CD hypotenuse.
DН = СD / 2 = 24/2 = 12 cm.
Answer: The length of the segment DH is 12 cm.
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