In an isosceles trapezoid, the acute angles are 60 degrees, the lateral side is 12cm and the larger base is 18cm

univerkov | March 14, 2021 | education

In an isosceles trapezoid, the acute angles are 60 degrees, the lateral side is 12cm and the larger base is 18cm. Find the smaller base and the midline of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. Lateral side AB = 12 cm. AD = 18 cm. BE – height to the base AD. ∠А = 60 °.

2. AE: AB = cosine ∠A.

AE = AB x cosine 60 ° = 12 x 1/2 = 6 cm.

3. In accordance with the properties of an isosceles trapezoid, the segment AE = (AD – BC): 2.

AD – BC = 2AE = 12 cm.

BC = AD – 12 = 18 – 12 = 6 cm.

4. Midline = (BC + AD) / 2 = (6 + 18): 2 = 12 cm.

Answer: BC = 6 cm, middle line = 12 cm.

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