Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises - Page 310: 4

(a) It is not possible to form two triangles. (b) If the line has length $L \gt 5$, we can draw exactly one triangle. (c) If $L \le 5$, we can draw no triangle.

(a) If the line has length $L \gt 5$, we can draw a line from the point to the positive x-axis. In this case we can only form one triangle because for each length $L \gt 5$, there is only one possible line from the point to the positive x-axis. It is not possible to form two triangles. (b) If the line has length $L \gt 5$, we can draw a line from the point to the positive x-axis. In this case we can draw exactly one triangle because for each length $L \gt 5$, there is only one possible line from the point to the positive x-axis. (c) If $L \le 5$, the line is not long enough to meet the positive x-axis, so we can draw no triangle.