Question

A landmark on a river bank is observed from two point A and B on the opposite bank of the river. The lines of sight make equal angles with the bank of river. if AB=1km.find the width of the river.

Answer 1

the width is 5 m long on the bank

Answer 2

Let PQ and MN be the two banks of a river and P be the landmark.

According to the given condition,

∠MPA = ∠NPB = 45º

⇒ ∠PAC = 45º [Alternate interior angle]

and ∠PBC = 45º [Alternate interior angle]

⇒ AP = BP [sides opposite to equal angles are equal]

Now, in triangles APC and BPC, we have

∠PAC = ∠PBC = 45º

AP = BP

and PC = PC [common]

⇒ AC = BC [c.p.ct]

or C is the mid point of AB.

Given, width of the river, AB = 1 km

Therefore, AC = BC = AB/2 = 1/2 km = 0.5 km