In the ABCD rectangle, the deogonal BD = 6 cm and forms 15 degrees with the side of AD.

univerkov | January 17, 2021 | education

In the ABCD rectangle, the deogonal BD = 6 cm and forms 15 degrees with the side of AD. Find the state from the top of C to the BD diagonal.

Let’s draw the second diagonal AC. Since the diagonals of the rectangle are equal, AC = ВD at the intersection point is divided in half, then the СOD triangle is isosceles ОС = OD = 6/2 = 3 cm.

Angle ADС = 90, then the angle ODС = СOD = 90 – 15 = 750. Then the angle СOD = 180 – 75 – 75 = 30.

CH is perpendicular to ВD, then the OCH triangle is rectangular, and the CH leg lies opposite the angle of 300, then CH = OC / 2 = 3/2 = 1.5 cm.

Answer: The distance from top C to the ВD diagonal is 1.5 cm.

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