The AC diagonal of the rectangular trapezoid ABCD is perpendicular to the side of the CD

| March 23, 2021 | education

The AC diagonal of the rectangular trapezoid ABCD is perpendicular to the side of the CD and makes an angle of 60 degrees with the base of AD. Find the height of the BA trapezoid if AD = 24.

According to the condition, the angle АСD is straight, and the angle DАС = 60, then the angle АDC = 180 – 90 – 60 = 30.

Then the leg AC of a right-angled triangle ACD lies opposite the angle 30, and then it is equal to half of the hypotenuse AD. AC = AD / 2 = 24/2 = 12 cm.

In a right-angled triangle ABC, the angle BAC = 90 – DAC = 90 – 60 = 30. Then the leg BC lies opposite an angle of 30, and its length is equal to half of the hypotenuse AC. BC = AC / 2 = 12/2 = 6 cm.

From a right-angled triangle ABC, leg BA = AC * Cos30 = 12 * √3 / 2 = 6 * √3 cm.

Answer: The height of the trapezoid is 6 * √3 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.