In the rectangle ABCD, the diagonal is AC = 8 * √3cm and forms an angle of 30 ° with the larger side of the rectangle.
| January 16, 2021 | education
In the rectangle ABCD, the diagonal is AC = 8 * √3cm and forms an angle of 30 ° with the larger side of the rectangle. find the sides of the rectangle.
In a right-angled triangle AСD, the angle СAD = 30. Then SinСAD = СD / AС.
СD = AC * Sin300 = 8 * √3 / 2 = 4 * √3 cm.
Determine the length of the AD leg.
Cos30 =AD / AC.
AD = AC * Cos30 = 8 * √3 * √3 / 2 = 12 cm.
The lengths of the opposite sides of the rectangle are equal, then AB = СD = 4 * √3 cm, BC = AD = 8 cm.
Answer: The sides of the rectangle are 4 * √3 cm, 8 cm.
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