In an isosceles trapezoid, the side is equal to the smaller base and the diagonal

In an isosceles trapezoid, the side is equal to the smaller base and the diagonal is perpendicular to the side. Determine the length of the diagonal if the length of the larger base is 2.

Let the values of the angles for a larger base be equal to X0. Triangle ABC, by condition, is isosceles since AB = BC, then AC is the diagonal of the angle BAD.

Angle ABC = DAC = X / 2.

In an isosceles trapezoid, the angles at the bases are equal, then the angle CDA = BAD = X0.

Triangle ABD is rectangular by condition, then the sum of its angles is: (X / 2 + X + 90) = 180.

3 * X / 2 = 90.

3 * X = 180.

X = CDA = 180/3 = 60, angle CAD = 60/2 = 30.

Cos30 = AC / AD.

AC = AD * Cos30 = 2 * √3 / 2 = √3 cm.

Answer: The length of the diagonal is √3 cm.