Acute angle of a rectangular trapezoid with a base of 6cm and 8cm = 45 degrees. Find the height of the trapezoid.

The height of the trapezoid is perpendicular to its base.

Consider the triangle ABM. The dac triangle is right-angled.

AM = AD – BC;

AM = 8 – 6 = 2 cm;

angle BAM = 45 °.

In a right-angled triangle, the sum of the acute angles is 90 °, which means:

angle ABM = 90 ° – BAM;

angle ABM = 90 ° – 45 ° = 45 °.

This means that the triangle ABM is also isosceles, since in isosceles triangles the angles at the base are equal.

This means that the leg BM = AM = 2 cm.

Answer: the height of the trapezoid BM = 2 cm.