Find the sides of the isosceles trapezoid. The bases of which are equal to 14 and 8 cm

univerkov | May 16, 2021 | education

Find the sides of the isosceles trapezoid. The bases of which are equal to 14 and 8 cm, and one angle is equal to 120 degrees.

1. The tops of the trapezoid – A, B, C, D. BC = 8 centimeters. BP = 14 centimeters. ∠В = 120 °. AB = CD.

BE is the height drawn to the base of AD.

2. Segment AE = (AD – BC) / 2 (according to the properties of an isosceles trapezoid).

AE = (14 – 8): 2 = 3 centimeters.

3. ∠ABE = 120 ° – 90 ° = 30 °.

4. We calculate the length of the lateral side AB through the sine ∠ABE:

AE: AB = sine ∠ABE = sine 30 ° = 1/2.

AB = AE: 1/2 = 3: 1/2 = 6 centimeters.

Answer: AB = CD = 6 centimeters.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.