(a) Is it possible to construct two noncongruent right triangles which each have one acute angle measuring 75 and a leg of 5cm on a side of the 75o angle?

Question

(a) Is it possible to construct two noncongruent right triangles which each have one acute angle measuring 75^o and a leg of 5cm on a side of the 75^o angle?

(b) Is it possible to construct two noncongruent triangles, each of which has angles measuring 30^o, 60^o, and 90^o?

(In other words, for each part, does the list of conditions describe only one possible triangle, or can there be different triangles which satisfy the conditions?)

Answer 1

a) Since both are right triangles with 90 and 75 degree angles, they are similar and the ratio of their corresponding sides are in proportion. Since the ratio of the sides opposite the 75 degree angle is 1 because the sides are equal, the other corresponding sides are also equal, so it is not possible to construct two non-congruent triangles in this situations.

b) The triangles are similar, but there is no restriction on the lengths of any sides except that they are in proportion, so many different non-congruent triangles could be constructed in this situation.