In a rectangular trapezoid ABCD with a right angle at apex A, the diagonals AC and BD

| September 3, 2021 | education

In a rectangular trapezoid ABCD with a right angle at apex A, the diagonals AC and BD are mutually perpendicular. Calculate the base length BC if the angle is BAC = 30 degrees, AD = 6 centimeters.

In a right-angled triangle ABC, we determine the value of the angle ACB.

Angle ACB = 180 – BAC – ABC = 180 – 30 – 90 = 60.

Angle CAD = ACB = 60 as criss-crossing angles at the intersection of parallel lines BC and AD secant AC.

In a right-angled triangle AOD, the angle ADO = 180 – OAD – AOD = 180 – 60 – 90 = 30, then the angle ADB = 30.

In a right-angled triangle, the AOD leg AO lies opposite the angle 30, and therefore is equal to half of the hypotenuse AD. AO = AD / 2 = 6/2 = 3 cm.

In a right-angled triangle AOB, the hypotenuse AB = AO / Cos 30 = 3 / √3 / 2 = 2 * √3 cm.

In a right-angled triangle ABC, we determine the length of the BC leg.

BC = tg30 * AB = (1 / √3) * 2 * √3 = 2 cm.

Answer: The length of the BC base = 2 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.