Question

(ii) Find the width of a river or a canal (without crossing it)

Answer 1

Answer:

Locate two objects at points  A  and  B  on either side of the river such that  AB  perpendicular to the the river and  B  is on your side of the river.

Walk a certain distance away from point  B  to a point  C  such that  A−B−C  and measure the distance  BC.  

Now walk a certain distance away from point  C  to a point  D  such that  BC⊥CD  and measure the distance  CD.  

Draw a figure of what is described above.

It can be seen that  ACD  is a right angled triangle.

Draw  BE∥CD,  such that point  E  lies on  AD.  

Walk from  B  to  E  and measure the distance  BE.  

It can easily be shown that  △ABE∼△ACD.  

⇒AB/AC=BE/CD  as they are the ratios of corresponding sides of similar triangles.

⇒AB/BC=BE/CD−BE.  

⇒AB=BC×BE/CD−BE,  where  AB  is the width of the river.