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 states that for a right - triangle with hypotenuse $c$ and legs $a$ and $b$, $a^{2}+b^{2}=c^{2}$. Here, $c = 12$ (length of the ladder) and $a = 4$ (distance of the base from the wall), and $b=h$. So, $h^{2}+4^{2}=12^{2}$.

Step2: Solve for $h^{2}$

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

Step3: Solve for $h$

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

Answer:

$11.3$ feet