Question

how high up the wall can a 12 - foot ladder reach if its base is 4 feet from the wall? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Apply Pythagorean theorem

Let the height up the wall be $h$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c = 12$ (length of ladder, hypotenuse) and $a = 4$ (distance of base from wall). So $4^{2}+h^{2}=12^{2}$.

Step2: Rearrange the equation

$h^{2}=12^{2}-4^{2}$. Calculate $12^{2}=144$ and $4^{2}=16$. Then $h^{2}=144 - 16=128$.

Step3: Solve for $h$

$h=\sqrt{128}\approx11.3$ (rounded to the nearest tenth).

Answer:

$11.3$ feet