## Law of Sines - the SSA case

*(please wait while the applet loads...)*

The interactive applet below shows why the SSA case in the
Law of Sines may have 0, 1, or 2 solutions. In this demonstration, we fix side *b*
(segment *AC* in the picture) and side *a* (segment *BC* in the picture),
and angle *alpha* (angle *DAC* in the picture). The initial picture shows
a situation which has no solution. With side *b* and angle *alpha* fixed,
you can rotate side *a* around the circle (drag point *B* with the mouse)
and see that no triangle can be created.

Drag point *D* to create another angle. Drag points *C*
and *B* to create different lengths for sides *a* and *b*. Note that
measurements are listed in the upper left corner. If the circle intersects ray *AD*
in two points, then two triangles can be created. If the circle intersects ray *AD*
in just one point, then only one triangle can be created (there are various ways
that this can happen). Experiment!

This page uses **JavaSketchpad**,
a World-Wide-Web component of *The
Geometer's Sketchpad**.* Copyright © 1990-2001 by KCP Technologies,
Inc. Licensed only for non-commercial use.

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SSA