Question

A student Ram wishes to find the width AB of the river without crossing it. His friend Shyam helps him to complete the task. Ram stands at point X just opposite to a fixed pole at A on the other side of the river, Shyam measures the distance between point X and B using a measuring tape. Now, he asked Ram to stand at a point C such that XB=YB. From point Y, he went perpendicular to the bank of river and reached to a point C such that A, B and C lies on the same straight line. He measures the distance YC and determines the width of the river. Justify the determination of width of river by measuring the distance YC

Answer 1

it is justified the determination of width of river by measuring the distance YC

Step-by-step explanation:

X is just opposite to A  

Hence ∠AXB =  90°

=> ∠BYC = 90°  given

XB = YB  given

ABC is in  a straight line

XBY is also in straight line

=> AC & XY intersect at B

hence ∠ABX = ∠CBY  ( opposite angles)

Now comparing triangle

ΔAXB    & ΔBYC

∠AXB = ∠BYC = 90

∠ABX = ∠CBY  ( opposite angles)

XB = YB

=> ΔAXB  ≅ ΔBYC

=> AX = YC

AX = width of river

=> YC =  width of river

Hence it is justified the determination of width of river by measuring the distance YC

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