An isosceles trapezoid is given. The side BC = 15, AD = 49cm is known, the angle D = 60

An isosceles trapezoid is given. The side BC = 15, AD = 49cm is known, the angle D = 60 degrees is also given. You need to find the perimeter of the trapezoid.

From the top of the trapezoid, we lower the height CH.

The height of an isosceles trapezoid, drawn from the top of an obtuse angle, divides the larger base into two segments, the smaller of which is equal to the half-difference of the bases, and the larger half-sum.

DН = (АD – ВС) / 2 (49 – 15) / 2 = 17 cm.

In a right-angled triangle СНD, the angle СDН = 60, then the angle DСН = 180 – 90 – 60 = 30.

Then the leg DH lies against the angle 30, and therefore is equal to half of the hypotenuse CD.

CD = 2 * DH = 2 * 17 = 34 cm.

Since the trapezoid is isosceles, AB = CD = 34 cm.

Determine the perimeter of the trapezoid.

P = AB + BC + CD + AD = 34 + 15 + 34 + 49 = 132 cm.

Answer: The perimeter of the trapezoid is 132 cm.



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