The bases of the isosceles trapezoid are 24 and 44, the cos of the acute angle of the trapezoid is 5/8. Find the side.

We will construct the heights of the ВН and СK of the trapezium AВСD.

Since the trapezoid is isosceles, then AB = СD, angle BAC = СDA, then the right-angled triangles ABН and СDK are equal in hypotenuse and acute angle.

Then AH = DK.

Quadrangle ВСKН is a rectangle, then НK = BC = 24 cm.

AH = (AD – KН) / 2 = (44 – 24) / 2 = 10 cm.

In a right-angled triangle ABН CosA = 5/8 = AH / AB.

AB = AH * 8/5 = 10 * 8/5 = 16 cm.

Answer: The length of the side is 16 cm.

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