ABCD rectangular trapezoid angle B rectangular BC = 5, AD = 3, AB = 3 find angle C

From the top D of the trapezoid, we draw the height of the BP.

In the formed right-angled triangle DHС, leg DH = AB = 4 cm, since they are the sides of the rectangle, leg HC = BC – BH = BC – AD = 5 – 3 = 2 cm.

Then the tangent of angle C is equal to the ratio of the opposite leg to the adjacent one.

tgC = DH / HC = 3/2 = 1.5.

Then the angle С = arctan (1.5) ≈ 56.

Answer: Angle С ≈ 56.