Question

1. when a ladder is 4.5 feet from the base of a wall, it just reaches the top of the wall, which is 9.625 feet high. how long is the ladder?

Explanation:

Step1: Identify the right - angled triangle

The distance from the base of the wall to the ladder is one leg ($a = 4.5$ ft), the height of the wall is the other leg ($b=9.625$ ft), and the ladder is the hypotenuse ($c$).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Substitute $a = 4.5$ and $b = 9.625$ into the formula: $c^{2}=4.5^{2}+9.625^{2}$.
$4.5^{2}=4.5\times4.5 = 20.25$ and $9.625^{2}=9.625\times9.625=92.640625$. Then $c^{2}=20.25 + 92.640625=112.890625$.

Step3: Find the length of the hypotenuse

Take the square - root of $c^{2}$ to find $c$. $c=\sqrt{112.890625}=10.625$ ft.

Answer:

$10.625$ ft