Longest side, widest corner

A triangular plastic sheet will cover the cycle stand before the monsoon. Its longest side gets the long rope. So the longest side must be found first.

Across from, not next to

Every side has one corner it does not touch. That corner is across from the side.

The longest side is across from the widest corner. The shortest side is across from the narrowest corner.

In the figure, 100 mm is across from the widest corner, 90°. The 60 mm side is across from the narrowest corner, 36.9°.

So the sheet needs no tape measure. Find the widest corner. The side across from it takes the long rope.

Look at each triangle. Which side is longest?