The bases of an isosceles trapezoid are 24 and 28. The cosine of an acute angle of a trapezoid is 2/5. Find the side.

Let’s call the trapezoid ABCD, where BC, AD are the bases, AB, CD are the sides. Let’s draw the heights BK and CL, we can find what AK and LD will equal, for this we find the difference in bases:
AK + LD = 28 – 24 = 4 cm;
Since AK and LD are equal, then the length of both AK and LD will be equal to 2 cm.
Consider one of the obtained right-angled triangles, namely AKB, we write down what the cosine of an acute angle is equal to, through the already existing side AK and unknown AB:
cos (BAK) = AK / AB;
2/5 = 2 / x;
x = 5 cm.
Answer: the length of the side is 5 cm.