Question

a 10 foot ladder leans against a wall. at the floor, it is six feet from the wall. how high up the wall does the ladder reach?

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the ladder is the hypotenuse (\(c = 10\) feet), the distance from the wall to the ladder on the floor is one leg (\(a = 6\) feet), and the height on the wall is the other leg (\(b\)) we need to find. We use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(b\)

We can rewrite the Pythagorean theorem as \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(c = 10\) and \(a = 6\) into the formula. First, calculate \(c^{2}=10^{2}=100\) and \(a^{2}=6^{2}=36\). Then, \(c^{2}-a^{2}=100 - 36=64\).

Step3: Calculate the square root

Now, find the square root of 64. \(\sqrt{64}=8\).

Answer:

The ladder reaches 8 feet up the wall.