Find the smaller diagonal of a rhombus whose sides are 49 and the acute angle is 60 degrees.

From the problem statement, it is known that the acute angle of the rhombus is 60 degrees, which means that the other obtuse angle is 120 degrees.
Let’s draw the second large diagonal of the rhombus. Consider a triangle formed by a rhombus side and half diagonals. The diagonals of the rhombus at the intersection point are halved and the diagonal of the rhombus divides the angle in half. Hence the angles of the resulting triangle are 30 degrees, 60 degrees and 90 degrees. Half of the smaller diagonal lies opposite an angle of 30 degrees, which means it is 49/2 = 24.5 cm. The smaller diagonal is 24.5 * 2 = 49 centimeters.