One of the corners of the parallelogram is alpha, and sides are a and b. find the diagonals of the parallelogram.

In a parallelogram, the sum of the angles adjacent to one side is 180 degrees. Therefore, if one of the angles of the parallelogram is α, then the second angle will be (180 – α).

The diagonals of a parallelogram form a triangle with its sides and they can be found by the cosine theorem: The square of any side is equal to the sum of the squares of the other two sides, without the double product of these sides by the cosine of the angle between them. a ^ 2 = b ^ 2 + c ^ 2 – 2bc * cos A.

d1 = √ (a ^ 2 + b ^ 2 – 2ab cos α);

d2 = √ (a ^ 2 + b ^ 2 – 2ab cos (180 – α)).