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

Answer: $\sqrt{101}$ feet or  10.05 feet.

Step-by-step 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

$(51)^2=(50)^2+b^2\\\\\Rightarrow\ b^2=(51)^2-(50)^2\\\\\Rightarrow\ b^2=2601-2500=101\\\\\Rightarrow\ b=\sqrt{101}=10.0498756211\approx10.05\ \text{[ Rounded to the nearest two decimal places. ]}$

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

Answer 2

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