In an isosceles trapezoid, the larger base is 2.7 m, the lateral side is 1 m, the angle between them

| September 9, 2021 | education

In an isosceles trapezoid, the larger base is 2.7 m, the lateral side is 1 m, the angle between them is 60 degrees. Find a smaller base.

Let us lower the BH height from the apex of the obtuse angle of the trapezoid. In a right-angled triangle ABН, by condition, the angle BAН is 60, then the angle ABН = 180 – 90 – 60 = 30. The leg AH is located opposite the angle 30, then its length is equal to half the length of the hypotenuse AB. AH = AB / 2 = 1/2 meter.

Let’s use the property of an isosceles trapezoid.

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

AH = (AD – BC) / 2.

1/2 = (2.7 – BC) / 2.

BC = 2.7 – 1 = 1.7 m.

Answer: The smaller base is 1.7 meters.



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