The acute angle of the rhombus is 60 degrees and the perimeter is 16. Find the length of the smaller diagonal.

1. The diagonal divides the acute angle of the rhombus in half:

60/2 = 30º.

2. For a rhombus, the lengths of all sides are equal. Knowing the perimeter, the side was found:

16/4 = 4.

3. The diagonals of a rhombus divide it into 4 equal right-angled triangles with a hypotenuse equal to the side of the rhombus and legs equal to half of the diagonals. Let’s denote half of the smaller diagonal “X”. Then:

Sin 30º = X / 4;

X = ½ * 4;

X = 2.

4. Find the length of the smaller diagonal:

2 * 2 = 4.

Answer: the length of the smaller diagonal is 4.