Question

One angle of a rhombus is 108 degrees and the shorter diagonal is 9 inches long. How long is the side of the rhombus

Answer 1

Now, for a rhombus, all sides are the same length, and the diagonals bisect the vertex they cut, so they cut them in halves, and they also meet at right-angles, and cut each other in halves as well

that means, if the angle is 108, the shorter diagonal will cut that in two equal angles, of 54 each, check the picture below

and since they each other cut in halves where they meet, one side of the shorter diagonal will then be half of 9, or 9/2 or 4.5

since the angle is in degrees, make sure your calculator is in Degree mode