In an isosceles trapezoid, the larger base is 42, the lateral side is 5, the angle between them

In an isosceles trapezoid, the larger base is 42, the lateral side is 5, the angle between them is 60 °, find the smaller base

Let ABCD be an isosceles trapezoid, let us drop heights from points C and D (see the figure below).
Since CDMN is a rectangle, then DC = MN
MN = AB – AM – BN.
Since triangles ADM and BCN are equal, AM = BN
MN = AB – 2 * AM
DC = AB – 2 * AM
AB = 42 by the problem statement, we find AM:
AM = AD * cos (60) = 5 * 0.5 = 2.5
DC = 42 – 2 * 2.5 = 42 – 5 = 37

Answer: 37.