Question

1. a 20 - ft pole is leaning up against the side of a barn. it is placed 5ft away from the base of the barn. how far up the side of the barn will the pole reach? draw a picture and show your work.

Explanation:

Step1: Identify the right - triangle

The pole, the ground, and the side of the barn form a right - triangle. The length of the pole is the hypotenuse $c = 20$ ft and the distance from the base of the barn to the bottom of the pole is one leg $a = 5$ ft. We want to find the other leg $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 5$ and $c = 20$ into the formula: $b=\sqrt{20^{2}-5^{2}}=\sqrt{400 - 25}=\sqrt{375}$.

Step3: Simplify the square - root

$\sqrt{375}=\sqrt{25\times15}=5\sqrt{15}\approx19.36$ ft.

Answer:

$5\sqrt{15}\approx19.36$ ft