Question

A 51-foot ladder is leaning up against a building . The top of the ladder reaches the wall at a height of 50 feet . How far is the bottom of the ladder from the building

Answer 1

if 50^2 +b^2=51^2 then
2500+b^2=2601
b^2=100
b=10

Answer 2

Answer:
`√(101)` feet or 10.05 feet.

Explanation:

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,

`l^2=h^2+b^2` , where h is the height of the wall , l 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+b^2\\\\\Rightarrow\ b^2=(51)^2-(50)^2\\\\\Rightarrow\ b^2=2601-2500=101\\\\\Rightarrow\ b=√(101)=10.0498756211\approx10.05\ \text{[ Rounded to the nearest two decimal places. ]}`

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