A rhombus of sides 20cm han an angled of 60degree, find the lenghts of its diagonals

20 cm and 34.64 cm.

Step-by-step explanation:

Consider the triangle with vertex 60 degrees. The diagonal is perpendicular to the other diagonal, and it bisects the 60 degree angle.

So we have the relation cos 30 = x / 20 where x = 1/2 of the diagonal.

x = 20 cos 30

x = 17.32

And as the diagonals bisect each other this diagonal = 2*17.32 = 34.64 cm.

Similarly, the other diagonal = 2 * 20 cos 60 = 20 cm