To measure the length of a table, the length of a car, or the width of
the classroom, you can walk from one end to the other, and you can
stretch a string or a tape measure the whole distance.
But if you need to measure the width of a river, there's no way to walk
a straight line between the ends of the measurement, and it's almost
impossible to use a ruler or a tape measure. You have to find another,
more clever way to measure it.
A little bit of trigonometry makes the job easy. I'll have to admit, though,
I don't immediately see where similar triangles would have to be involved.