A 51 foot ladder is leaning up against a building the top of the ladder reaches the wall at a height of 50 ft how far from the bottom of the ladder from the building?

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We know that wall stands vertical to the ground makes right angle.

Then, the triangle made by ladder must be right triangle.

Now, by Pythagoras theorem of right triangle we have,

1² h² + b², where h is the height of the wall, I is length of ladder and b is the distance of bottom from the building.

By considering the given information, we have

(51)² = (50)² +

⇒ 6² = (51)² (50)²

→ 6² = 2601 2500 = 1

⇒ b = 101 = 10.0498756211 ≈ 10.05

Hence, the distance of bottom from the building = 10.05 feet.