Parallelogram ABCD gives: AD = 2, angle BAD = 60 degrees
| September 19, 2021 | education
Parallelogram ABCD gives: AD = 2, angle BAD = 60 degrees, BE perpendicular to AD, BE = 2√3. find the length of the larger diagonal of the parallelogram.
Since BE is perpendicular to AD, then triangle ABE is rectangular, then:
SinVAE = BE / AB.
AB = CD = BE / SinBAE = 2 * √3 / √3 / 2 = 4 cm.
The sum of the adjacent angles of the parallelogram is 180, then the angle ADC = 180 – 60 = 120.
From the triangle ACD, by the cosine theorem, we determine the length of the AC.
AC ^ 2 = AD ^ 2 + CD ^ 2 – 2 * AD * CD * CosADS.
AC ^ 2 = 4 + 16 – 2 * 2 * 4 * (-1 / 2) = 20 + 8 = 28.
AC = √28 = 2 * √7 cm.
Answer: The length of the larger diagonal is 2 * √7 cm.
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