SOMEBODY PLEASE HELP ME: Determine which side is the shortest in each diagram:

Mathematics

2 answers:

Art [367]3 years ago

7 0

In any triangle, the smallest side and smallest angle are opposite one another.

so in triangle DFG the shortest side is DG because it is opposite 52 degrees

in triangle EFG the shortest side is EG because it is opposite 47 degrees

I AM USING THE NUMBER IN THE DIAGRAM. i ASSUME THEY ARE CORRECT?

DG< EG

Juliette [100K]3 years ago

4 0

Answer:

DG is the shortest side.

Step-by-step explanation:

The problem can also be solved by using sine rule:

sin47/EG = sin48/FG = sin85/EF

So EG is the shortest in triangle EFG

In triangle DEG, sin52/DG = sin67/EG = sin61/DE

So DG is the shortest side and it is equal to:

DG = EG*sin52/sin67

Because sin52/sin67 < 1, DG < EG

DG is the shortest side.

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