Let’s call the triangle ABC (AC – base, AB = BC).
In an isosceles triangle, the angles at the base are equal. Angle B = 120, which means angle A = angle C = (180 – 120) / 2 = 30 degrees.
Let’s draw the height of the ВН. In an isosceles triangle, BH is also the median, which means that AH = CH = 36/2 = 18 cm.
Consider a triangle BCH: angle c = 30 degrees, CH = 18 cm.
Let us express the cosine of the angle C = CH / BC.
cosC = 18 / ВС
cos 30 = 18 / ВС
ВС = 18 / cos30 = 18 / (√ 3/2) = 36 / √ 3
Multiply the numerator and denominator by square. root of 3 to get rid of the irrationality of expression.
(36 * √ 3) / 3 = 12 * √3.
Answer: the side edge of the triangle is 12 * √ 3.
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