Question

How far up a wall a 10m ladder fall if it is 4 cm away from the wall + triangle properties?

Answer 1

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

Answer 2

H^2= B^2+P^2

10^2=0.04+P^2

P^2=100-0.004

P^2= 99.99