One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. approximately how long is the side of the rhombus?

A rhombus is a quadrilateral which has 4 equal sides but two pairs of unequal angles.  We are given one of the angles to be equal to 102 degrees so the other angle would have a measurement of 78 degrees. We calculate the length of the side as follows:
Triangle that is formed by two sides of rhombus and smaller diagonal is an isosceles triangle.
 
vertex angle = 78°
base angles = 51°
side opposite the vertex angle = 4
sides opposite the base angles = x 

Using the law of sines,
x/sin(51) = 4/sin(78) 
x = 4 * sin(51)/sin(78) 
x = 3.18

Therefore, the length of the side would be 3.18.