In parallelogram ABCD, side AB equals 6 roots of 2 cm, diagonal BD equals 6 roots of 3 cm
| April 24, 2021 | education
In parallelogram ABCD, side AB equals 6 roots of 2 cm, diagonal BD equals 6 roots of 3 cm, forms an angle of 45 degrees with side AD.Find the angles of the parallelogram.
Determine the value of the angle BAD by the theorem of sines.
ВD / SinВAD = AB / SinADВ.
SinBAD = BD * SinADB / AB = (6 * √3 * √2 / 2) / 6 √2 = √3 / 2.
Angle BAD = arcsin (√3 / 2) = 60.
Since the parallelogram has opposite angles, the angle ВСD = BAD = 60.
The sum of the adjacent angles of the parallelogram is 180, then the angle ABC = 180 – 60 = 120.
Answer: The angles of the parallelogram are 60 and 120.
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