Final answer:
The longer diagonal of the rhombus is 19.1 cm.
Step-by-step explanation:
In a rhombus, the longer diagonal is equal to twice the length of the shorter diagonal. So, we need to find the length of the shorter diagonal in order to find the longer diagonal. Since we are given the length of the side of the rhombus, we can use the trigonometric relationship of the diagonals in a rhombus to find the shorter diagonal.
Using the formula for the shorter diagonal, d = 2L sin(angle), where d is the shorter diagonal, L is the length of the side, and angle is the obtuse angle, we can substitute the given values and calculate:
d = 2(14 cm) sin(160°) = 2(14 cm) (-0.342) = -9.55 cm
The length of the longer diagonal is twice the length of the shorter diagonal, so the longer diagonal is 2(-9.55 cm) = -19.1 cm. However, since length cannot be negative, the longer diagonal of the rhombus is 19.1 cm.