Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises - Page 305: 32

If $\frac{a~sin~B}{b}\gt 1$, then there is no triangle satisfying the given values, because there is no angle $A$ such that $sin~A \gt 1$

Given $a, b,$ and $B$, we can use the law of sines to find the angle $A$: $\frac{b}{sin~B} = \frac{a}{sin~A}$ $sin~A = \frac{a~sin~B}{b}$ If $\frac{a~sin~B}{b}\gt 1$, then there is no triangle satisfying the given values, because there is no angle $A$ such that $sin~A \gt 1$