A rectangular trapezoid is given. Smaller side of a rectangular trapezoid = 10cm. Acute angle = 45. Find the second side.

Let us draw the height CH from the top of the trapezoid. According to the condition, the СDН angle = 450, then the НСD angle = 180 – 90 – 45 = 450, therefore, the СDН triangle is isosceles and rectangular, CH = DН.
Since ABCН is a rectangle, then CH = AB = 10 cm.
And in a right-angled triangle СНD, according to the Pythagorean theorem, we determine the length of the hypotenuse of the СD.
СD2 = CH2 + DН2 = 100 + 100 = 200.
СD = √200 = 10 * √2 cm.
Answer: The second side is 10 * √2 cm.

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