Question

1. scott is building a set of stairs off the back of his deck. he measured the height of the deck as 12 feet high and wants the stairs to be 24 feet long. how far away from the house (horizontally) will the stairs end? round to the nearest hundredth.

Explanation:

Step1: Identify the problem as a right - triangle problem

We can consider the height of the deck as one leg ($a = 12$ feet), the horizontal distance from the house as the other leg (let's call it $b$), and the length of the stairs as the hypotenuse ($c = 24$ feet) of a right - triangle. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We get $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 12$ and $c = 24$ into the formula: $b=\sqrt{24^{2}-12^{2}}=\sqrt{(24 + 12)(24 - 12)}=\sqrt{36\times12}=\sqrt{432}$.

Step3: Calculate the value of $b$

$\sqrt{432}\approx20.78$ feet.

Answer:

$20.78$ feet