An Ambiguous Case of Triangle Construction
Move the point FreeLine to invsetigate where your hook ends up.
Use the sliders to adjust the values to investigate the following possibilities:
If the Line is less than the Height (Line<Height), then there is no triangle possible (NO solution)
If the Line exactly equals the Height (Line=Height), there is a right-triangle (ONE solution)
If the Line is longer than the height but shorter than the rod (Height<Line<Rod), there are TWO solutions
If the Line is equal to or longer then the Rod (Line>=Rod) then there is ONE solution

Adapted from dweppler's Worksheet by Kathryn Brenneman for MA 111 at NCSU.