the foot of a ladder is 6m away from a wall and it's top reaches a window 8m above the ground if the ladder is shifted in such a way that it's foot is 8m away from the wall. So what height does it's top reach?
kvnmurty:
Let A be the foot of the ladder. B be the top of the ladder. C be the junction/corner of the wall and floor. AB = 6m, BC = 8 m... When AB = 8m.. Then BC becomes 6m., The sides AB and BC are interchanged, as the length AC is constant.
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Answered by
419
The 'ladder', 'height to which it reaches' and 'foot of ladder from wall' forms a right angled triangle.
ladder = hypotenuse(h)
height to which it reaches = base(b)
foot of ladder from wall = altitude(a)
initially, a = 8m, b = 6m
h² = a² + b²
⇒ h = √(a²+b²) = √(8² + 6²) = √100 = 10m
when foot is 8m away from wall,
b = 8m, h = 10m, a = ?
h² = a² + b²
⇒ a² = h² - b²
⇒ a = √(h² - b²) = √(10² - 8²) = √36 = 6m
So its top reaches 6m height
ladder = hypotenuse(h)
height to which it reaches = base(b)
foot of ladder from wall = altitude(a)
initially, a = 8m, b = 6m
h² = a² + b²
⇒ h = √(a²+b²) = √(8² + 6²) = √100 = 10m
when foot is 8m away from wall,
b = 8m, h = 10m, a = ?
h² = a² + b²
⇒ a² = h² - b²
⇒ a = √(h² - b²) = √(10² - 8²) = √36 = 6m
So its top reaches 6m height
Answered by
206
6 Metres
6m sq + 8 m sq=x m sq
100 m = x m sq
x= 10 m= length of ladder
base= 8 m length of ladder= 10 m
therefore height from ground to top = uder root of( 10 m sq - 8 m sq)= 6METRES
6m sq + 8 m sq=x m sq
100 m = x m sq
x= 10 m= length of ladder
base= 8 m length of ladder= 10 m
therefore height from ground to top = uder root of( 10 m sq - 8 m sq)= 6METRES
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