In an isosceles trapezoid ABCD, the side is AB = 4cm, BE is the height, and the angle ABE = 30 degrees. Find the height CF.

Isosceles is a trapezoid in which the sides are equal:

AB = CD.

Since the bases of the trapezoid are parallel, the heights of the trapezoid are equal to each other:

BE = CF.

In order to find the length of the height BE, consider the triangle ΔABE.

Since we know the value of the angle ∠ABE and the length of the hypotenuse AB, we will use the cosine theorem to calculate BE:

cos B = BE / AB;

BE = AB cos B;

cos 30º = 0.866;

BE = 4 · 0.866 = 3.464 ≈ 3.5 cm;

CF = BE = 3.5 cm.

Answer: The length of the CF height is 3.5 cm.