In an isosceles trapezoid, one of the acute angles is 60, the length of the lateral side

univerkov | August 5, 2021 | education

In an isosceles trapezoid, one of the acute angles is 60, the length of the lateral side is 16 cm. Find the bases of the trapezoid if their sum is 38 cm.

1. A, B, C, D – the tops of the trapezoid. AB = 16 cm. ∠A = 60 °. ВС + АD = 38 cm. ВР – height to the base АD.

2. ∠АВР = 180 ° – ∠А – ∠АРВ = 180 ° – 60 ° – 90 ° = 30 °.

3. AR: AB = sine 30 ° = 1/2.

AR = AB x 1/2 = 16 x 1/2 = 8 cm.

4. In accordance with the properties of an isosceles trapezoid, AR = (AD – BC) / 2.

AD – BC = AP x 2 = 8 x 2 = 16 cm.

AD = BC + 16 cm.

5. Substitute АD = ВС + 16 cm into the expression given in the problem statement:

BC + BC + 16 = 38 cm.

BC = 11 cm.

AD = 11 + 16 = 27 cm.

Answer: BC = 11 cm. AD = 27 cm.

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