In a rectangular trapezoid ABCD with bases AD and BC, angle A = angle B = 90 degrees. angle АCD

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

1. Draw the CE height.

2. CE divides the trapezoid into two geometric shapes: rectangle ABCE and right triangle BDE.

3. The sides of the rectangle that are opposite each other (opposite) are equal, that is, AE = BC = 4 cm.

4. DE = 16 – 4 = 12 cm.

5. The height drawn from the top of the right angle is calculated by the formula:

CE = √4 x 12 = √48 = 4√3 cm.

6.CEDE = tangent ∠D = 4√3 / 12 = √3 / 3.

∠D = 30 °, since tangent 30 = √3 / 3.

∠С = 180 ° – 30 ° = 150 °.

Answer: ∠D = 30 °, ∠С = 150 °.