Measuring the River

[Quote:]

A traveler reaches a river at the point A and wishes to know the width across to B. As he has no means of crossing the river, what is the easiest way of finding its width?

Answer below the fold

“Measure any convenient distance along the bank from A. to C, say 40 yards. Then measure any distance perpendicularly to D, say 12 yards. Now sight along DB and find the point E. You can then measure the distance from A to E, which will here be 24 yards, and from E to C, which will be 16 yards. Now AB:DC = AE:EC, from which it is evident that AB, the width of the river, must be 18 yards.”

2 Responses to “Measuring the River”

  1. Mauro Says:

    Hm. I think trig would be easier. Find any other point C along the river, and measure the distance to it. Then find the angles at A and C (and therefore at B), and Law of Sines to find AB. I think similar triangles would have to involve a lot more measuring…

  2. Roland Hesz Says:

    I am always amazed that people travel around with a measuring pole, a trigonometrical kit, measuring tapes, lenses, and all the stuff they need to do these things.

    I usually measure rivers like “narrow, wide, bloody wide, Danube, Tisza” :)


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