Answer:
27.57 in
Step-by-step explanation:
You want the length of the longer diagonal of a rhombus with side lengths 14 inches and obtuse angle 160°.
Law of Cosines
The law of cosines can be used to find the diagonal length. The length of the third side (c) is given by ...
c² = a² +b² -2ab·cos(C)
where a and b are the other two sides, enclosing angle C.
Application
c² = 14² +14² -2·14·14·cos(160°)
c² = 392 -392·cos(160°) ≈ 760.35951
c ≈ 27.5746
The longer diagonal is about 27.57 inches long.
