isosceles trapezoid ABCE,
BC = 6 centimeters,
AE = 12 centimeters,
angle A = angle E = 60 degrees.
Find the length of the side, that is, AB -?
1. Consider an isosceles trapezoid ABCE. Let’s draw the heights BH and CO. We get the HBCO rectangle. He has BH = CO and BC = HC = 6 centimeters.
2. Right-angled triangle AH = right-angled triangle COE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then CE = AH = (12 – 6): 2 = 6: 2 = 3 (centimeters).
3. Consider the BHA triangle. Angle ABH = 180 – 90 – 60 = 30 (degrees). The leg, which lies opposite an angle of 30 degrees, is equal to half of the hypotenuse, that is, AB = 2 * AH = 2 * 3 = 6 (centimeters).
Answer: 6 centimeters.
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