In an isosceles trapezoid, a smaller base = 6cm side = 4cm and a sharp angle = 60 degrees Find a large base.

Consider an isosceles trapezoid ABCD, where

greater base AD,

smaller base BC = 6 cm,

sides AB = CD = 4 cm and

and an acute angle BAC = 60 °.

Let us lower the height BH from the top B to the larger base AD.

Triangle ABH – rectangular with right angle BHA. Therefore:

AH = AB * cos (BAC) = 4 * cos (60 °) = 4 * (1/2) = 2.

Similarly, let us lower the CM height from the top C to the larger AD base.

Triangle CDM – rectangular with right angle CMD. Therefore:

MD = CD * cos (CDM) = 4 * cos (60 °) = 4 * (1/2) = 2.

Therefore, we have that the big base AD:

AD = AH + HM + MD = AH + BC + MD = 2 + 4 + 2 = 8.