In an isosceles trapezoid, the bases are 2 cm and 18 cm. The lateral side is 16 cm. Find an acute angle at the base.

univerkov | August 2, 2021 | education

1. A, B, C, D – the tops of the trapezoid. BC = 2 centimeters. AD = 18 centimeters. AB = 16 centimeters. BE – height to the base of AD.

2. In accordance with the properties of an isosceles trapezoid, the segment AE = (AD – BC) / 2 = (18 – 2): 2 = 8 centimeters.

AE: AB = sine ∠ABE.

AE: AB = 8: 16 = 1/2.

∠ABE whose sine is 1/2 is 30 °.

3. ∠А = 180 ° – 90 ° – 30 ° = 60 °.

Answer: ∠A acute angle at the base of the trapezoid is 60 °.

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