ABCD is a rectangular trapezoid (angle D = angle C = 90 degrees) BC = 2, AD = 4, CD = 2√3. Find angle A

1. ВН – height (drawn to the base of AD).

2. The height BH is the side of the rectangle BCDH, the opposite sides of which are equal:

ВH = СD = 2√3 units of measurement. BC = DH = 2 units.

3. Segment АН = АD – DH = 4 – 2 = 2 units of measurement.

4. Calculate the tangent ∠A of the right-angled triangle ABN, in which BH and AH are legs.

BH: AH = tangent ∠A.

Tangent ∠A = 2√3: 2 = √3. An angle whose tangent is √3 is 60 °.

∠А = 60 °.

Answer: ∠А is equal to 60 °.