In an isosceles trapezoid, one of the angles is 60 degrees, and the base is 15cm and 49cm. Find its perimeter.

The perimeter of a trapezoid is equal to the sum of its sides:

P = AB + BC + CD + AD.

Since the trapezoid is isosceles, then:

AB = CD;

AH = KD.

In this way:

AH = KD = (AD – BC) / 2;

AH = KD = (49 – 15) / 2 = 34/2 = 17 cm.

Consider a triangle ∆АВН.

To calculate the side AB, we use the cosine of the angle ∠A:

cos A = AH / AB;

AB = AH • cos A;

cos 60 ° = 1/2 = 0.5;

AB = 17 / 0.5 = 34 cm.

P = 34 + 15 + 34 + 49 = 132 cm.

Answer: the perimeter of the trapezoid is 132 cm.