ABCD-isosceles trapezoid AD = 12 cm BC = 6 cm angle A = 60 degrees Find: AB CD -?

univerkov | August 17, 2021 | education

1. BE – height (drawn to the base of AD).

2. According to the properties of an isosceles trapezoid, the length of the segment AE is calculated by the formula:

AE = (AD – BC) / 2 = (12 – 6): 2 = 3 cm.

3. We calculate the length of the side AB of the trapezoid through the cosine ∠ABE, equal to the quotient of the division of the segment AE (leg of the right-angled triangle ABE) by AB (the hypotenuse of the indicated triangle):

BE: AB = cosine ∠ABE = cosine 60 ° = 1/2.

AB = BE: 1/2 = 3: 1/2 = 6 cm.

Answer: AB = CD = 6 cm – lateral sides of an isosceles trapezoid.

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