Find the smaller lateral side of a rectangular trapezoid, the bases of which are 16cm and 28cm, if one of the corners is 45 degrees.

| December 3, 2020 | education

Take ABCD – a rectangular trapezoid, where AD = 28 cm, BC = 16 cm
To solve this problem, you need to draw the height (CH) from the angle ВСD to the base АD
1) Consider ABCH.
BC = AH = 16 cm
2) a segment of blood pressure is equal to the sum of two segments (AH and HD), i.e. find НD
28 cm = 16 cm + НD
НD = 12 cm.
3) Consider a triangle СНD
Because we held the altitude CH. then the angle СНD = 90 degrees, i.e. the triangle СНD is rectangular.
It is known that the angle СDН = 45 degrees, then the angle НСD = 45 degrees (the sum of acute angles in a right-angled triangle is 90 degrees). So the sides CH and DH are equal, and CH = 12 cm.
4) find the SMALL side side of the trapezoid.
СD = HD / сos 45 = 12√2 – large side
AB = CH = 12 cm – smaller side
ANSWER: 12 cm



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