In triangles △ABC and △DEF, m∠A=m∠E, m∠C=m∠F, AC=6, EF=2, and AB=3.3, side DF is shorter than side BC by 3.2. Find the unknown sides of these triangles.

Answer 1

I am not going to solve this for you, but I will tell you how to do it.

The critical fact is that the 2 triangles are similar. Why? 2 pairs of angles are stated to be equal; therefore, the third angle are equal also. That makes the two triangles similar.

AC;EF = 6:2 and therefore, ED = 1.1.

DF + 3.2 = BC and BC:DF = 3. With these 2 equations you can get the 2 remaining side.