Find the area of a rectangle if one of its sides is 5 cm. And the angle between the diagonals is 60 degrees.

From the condition of the problem, we know that one of the sides of the rectangle is equal to a = 5 centimeters. We also know that the angle between the diagonals of this rectangle is 60 degrees. Knowing this information, we need to find the area of the rectangle. To do this, we need to use the formula:

S = (d ^ 2 * sin a) / 2

Where d is the length of the diagonal of this rectangle.
But we don’t know the diagonal. It can be found from the formula:

a = d * sin a / 2
d = a / (sin a / 2) = 5 / sin 30 = 5 / (1/2) + 5 * 2/1 = 10

Then the area of the rectangle is:

S = (d ^ 2 * sin a) / 2 = (10 ^ 2 * sin 60) / 2 = (100 * √3 / 2) / 2 = √3 * 50/2 = 25√3