Question

the foot of a ladder is placed 6 feet from a wall. if the top of the ladder rests 8 feet up on the wall, how long is the ladder?

Explanation:

Step1: Identify Pythagorean theorem

The ladder, wall, and ground form a right triangle. Use $a^2 + b^2 = c^2$, where $a=6$, $b=8$, $c$ is ladder length.

Step2: Substitute values into formula

$$6^2 + 8^2 = c^2$$
$$36 + 64 = c^2$$

Step3: Solve for $c$

$$100 = c^2$$
$$c = \sqrt{100} = 10$$

Answer:

10 feet