The lateral trapezoid of an isosceles trapezoid is 10 cm, height 8 cm. Find the cosine of the acute angle of the trapezoid.

Perhaps you meant the side of an isosceles trapezoid. Then assume that the height comes from the intersection of the smaller base and the side. And then the lateral side is the hypotenuse, and the height is the leg. And the third side is also a leg. Then this third side that is part of the base is equal to the root of (10 ^ 2 – 8 ^ 2) = √ (100-64) = √ 36 = 6
Now we find the cosine of an acute angle, this must be divided by the third side (6) by the hypotenuse (10) = 0.6
According to the cosine table, this is 53 degrees