Final answer:
The length of the longer diagonal of the rhombus is 28 inches.
Step-by-step explanation:
A rhombus is a quadrilateral with all sides of equal length. In a rhombus, each pair of opposite angles are equal. The measure of each obtuse angle in the rhombus is given to be 160 degrees. To find the length of the longer diagonal of the rhombus, we can use the properties of a rhombus.
Since the opposite angles in a rhombus are equal, the measure of the acute angles is equal to (180 - 160) / 2 = 10 degrees.
The longer diagonal of a rhombus can be found using the formula d = 2 * s * sin(theta), where d is the length of the diagonal, s is the length of one side, and theta is the measure of one of the acute angles. Plugging in the values, we get d = 2 * 14 * sin(10) = 28 inches.