A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
Let the length of the ladder = AC = 5 m
Let the height of the wall on which ladder is placed = BC = 4m.
From right-angled ∆EBD,
Using the Pythagoras Theorem,
ED2 = EB2 + BD2
(5)2 = (EB)2 + (14)2 ......[BD = 1.4]
25 = (EB)2 + 1.96
(EB)2 = 25 – 1.96 = 23.04
EB = `sqrt(23.04)` = 4.8
Now, we have,
EC = EB – BC
= 4.8 – 4
Hence, the top of the ladder would slide upwards on the wall by a distance of 0.8 m.
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
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