Answer:
The ladder will go approximately 35.71 ft up the building.
Step-by-step explanation:
The 50 ft ladder is leaning against a building and the base of the ladder is 35 feet from the base of the building.
It means the ladder will form a right triangle with the building with the following dimensions:
Using the Pythagorean Theorem to determine the height,
[tex]a^2+b^2=c^2[/tex]
Here,
Substitute the given values into the equation to determine the height:
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+\left(35\right)^2=\left(50\right)^2[/tex]
[tex]a^2+1225=2500[/tex]
[tex]a^2=1275[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]a=\sqrt{1275},\:a=-\sqrt{1275}[/tex]
[tex]a\:=\:35.71,\:\:\:a\:=\:-35.71[/tex]
We know that height can not be negative. Thus,
[tex]a=35.71[/tex] ft
Therefore, the ladder will go approximately 35.71 ft up the building.
