Anonymous

# Help with maths problem?

Napoleon is marching along flat ground with troops, and they come to a river. Napoleon wants to know the width of the river before they cross (though I'd be more concerned about the depth!). Anyway, one of the soldiers steps up to the edge of the river and faces directly across the water. He adjusts his cap until the tip of the visor is in line with his eye and the edge of the opposite bank. Then he turns around and faces away from the river. He notes the spot on the ground that is ow in line with his eye and the tip of his visor, an paces off that distance, announcing that it is equal to the width of the river.

Does this method work in theory?

Relevance

Yes. This uses the ASA theorem of triangle congruence.

The soldier is presumed to stand at a 90 degree angle to the ground, forming one angle. The soldier's height is constant, forming the side. The adjustment of the soldier's cap forms the third angle.

When the soldier turns he is presumed to maintain his head position perfectly.

Now we have two congruent triangles. Since corresponding parts of congruent triangles are congruent, the distance the soldier paces on the ground is equal to the width of the river.