One triangle has a known angle and two known side lengths. Another triangle has two known angles and one known length and the third triangle only has three known lengths and no known angles. Is it possible to construct a different (noncongruent) triangle using the same parts (the new triangle must contain only the parts from one of the current triangles)

Question

wolf1728 · Answer

In case 1 - there can be 1 or 2 triangles formed See the link here: http://1728.org/trigssa.htm In case 2, since two angles are known it is easy to calculate the third angle. In case 3, three known sides, it follows the congruence theorem that only 1 triangle may be formed. (It's possible that NO triangle could be formed from sides of length 2, 5 and 100 for example.)

anonymous · Answer

ok, I understand case 2 and 3... but I still can't figure out how to get two triangles from case 1. Lets say that the known angle is 55 degrees and that the known lengths are 3.5 cm and 6.5 cm. Can you help me with this please?

wolf1728 · Answer

Using my calculator at the link posted above, inputting a 55 degree angle and sides 3.5 and 6.5 cm yields only 1 solution.
So, I tried inputting my own numbers:
angle = 45° sides = 7 and 5
and obtained two solutions.
The attached graphic should be quite a help to you.

wolf1728 · Answer

Here's another good link - this goes to Wikipedia https://en.wikipedia.org/wiki/Side-Side-Angle#Two_sides_and_non-included_angle_given_.28SSA.29 It explains all possible tests for congruence. case 1 is side side angle SSA case 2 is angle angle side which can easily be converted to angle side angle case 3 is side side side

anonymous · Answer

Thanks Wolf... got it now.