D. The Sine Law and the Ambiguous Case
Completion requirements
D. The Sine Law and the Ambiguous Case
When solving a triangle, given two sides and an angle not contained within those sides (SSA triangle), using the sine law may result in solutions that are ambiguous – a situation where more than one solution is possible.
Open the Ambiguous Case applet.
Investigate what happens when you change the length of side \(a\) using the slider and when you move its ending position by clicking and dragging the red dot.
Investigation |
Ambiguous Case
Open the Ambiguous Case applet.
Investigate what happens when you change the length of side \(a\) using the slider and when you move its ending position by clicking and dragging the red dot.
- What values of \(a\) do not produce a triangle?
- What values of \(a\) produce a right triangle?
- What values of \(a\) produce only one triangle?
- What values of \(a\) produce two triangles?
- Calculate \(b \sin A\). What do you notice about its value and your answers to questions 1 to 4?