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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?
- davide405Lv 51 decade agoFavorite Answer
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.
- 1 decade ago
soldier used the trigonometry.Angle of declanation was measured by the soldier as per the method above and calculated the width.In trigonometry if perpendicula,hypotenuse and the angle between hypotenuse and perpendicular is known then base can be calculated.
Here soldiers height is perpendicular,angle of declanation set be cap and he has calculated the base (width of river).When he turns round all are same and the triangle is reversed.Thus calculated the width by measuring distance at land.