In a rectangular trapezoid ABCD with a base AD and BC, the angle A = angle B = 90

| May 18, 2021 | education

In a rectangular trapezoid ABCD with a base AD and BC, the angle A = angle B = 90, angle ACD = 90, BC = 4 cm, AD = 16 cm.Find the angles C and D of the trapezoid.

Let us draw the height of CH from the vertex C of the trapezoid. Quadrangle ABСН is a rectangle, since the trapezoid is rectangular, and CH is the height of the trapezoid, then AH = BC = 4 cm.

Then DH = AD – AH = 16 – 4 = 12 cm.

The ACD triangle is rectangular, since, according to the condition, the ACD angle is straight. Then the height of the CH in the ACD triangle is drawn from a right angle to the hypotenuse. Then CH ^ 2 = AH * DH.

CH ^ 2 = 4 * 12 = 48. CH = 4 * √3 cm.

Then in a right-angled triangle СНD tgD = СН / DH = 4 * √3 / 12 = √3 / 3.

Angle ADC = arctan (√3 / 3) = 30.

In a right-angled triangle ABC tgC = AB / BC = 4 * √3 / 4 = √3.

Angle ACB = arctan (√3) = 60. Then angle BCD = 60 + 90 = 150.

Answer: The ADC angle is 30, the BCD angle is 150.



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.