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
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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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