In the adjoining figure, explain how one can find the breadth of the river without crossing it.
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Given:

$AB$ is the breadth of the river.

To do:

We have to find how one can find the breadth of the river without crossing it.

Solution:

Take a point M at a distance from B.

Draw a perpendicular from the point M and name it as N so that it joins the point A as a straight line.

In $\triangle ABO$ and $\triangle NMO$

We know that,

$\angle OBA = \angle OMN = 90^o$

O is the midpoint of the line BM.

This implies,

$OB = OM$

From the figure,

$\angle BAO$ and $\angle MON$ are vertically opposite angles

$\angle BAO = \angle MON$

$\triangle ABO \cong \triangle NMO$   (By ASA congruence)

$AB = NM$     (CPCT)

Therefore, MN is the width of the river.

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Updated on: 10-Oct-2022

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