SSA Cases
- Author:
- jnovogoratz
The triangle below allows you to change two sides (a, b) and an angle not included between them (B). Play around with the applet before looking at the questions; as you play, specifically make observations about the possible triangles ABC that appear (namely, be on the look-out for "A")
1) The default settings result in one possible triangle ABC.
1.a) What is the angle classification (acute, right, obtuse, equiangular) of triangle ABC?
2) Make B obtuse (greater than 90). Change the relative values of sliders for "a" and "b." [Relative value: less/greater than or equal to, etc.]
2.a) What do you notice about the relative values of "a" and "b" when there is one possible triangle ABC?
2.b) What do you notice about the relative values of "a" and 'b" when there are no possible triangles ABC?
3) Setting b<a and B acute (less than 90), there are two possible triangles ABC; in both, the height (CH) is the same.
3.a) In right triangle BHC, which side is the hypotenuse?
3.b) Is the height CH opposite or adjacent to angle B?
3.c) Using sin/cos and any combination of a, b, and/or B, what is the length of height CH?
4) Set B acute (less than 90).
4.a) Setting b=a, how many possible triangles ABC are there: zero, one, or two?
4.b) Setting b>a, how many possible triangles ABC are there: zero, one, or two?