In an isosceles trapezoid, the smaller base is 6 lateral side 13, and one of the 120 degree angles, find the smaller base.

univerkov | March 10, 2021 | education

Let’s build the height of the HВ trapezoid.

In a right-angled triangle ABН, the angle ABН = ABC – СВН = 120 – 90 = 30.

The leg AH lies against an angle of 30, then AH = AB / 2 = 13/2 = 6.5 cm.

AH in an isosceles trapezoid is also equal to: AH = (AD – BC) / 2.

Then: AD = 2 * AH + BC = 2 * 6.5 + 6 = 19 cm.

Answer: The larger base is 19 cm.

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