Question

how high up the wall does the ladder touch? 144 194 13.9 12

Explanation:

Step1: Identify the problem as a right - triangle problem

The ladder, the wall and the ground form a right - triangle. Let the distance from the base of the ladder to the wall be the base $a = 1$ meter and the length of the ladder be the hypotenuse $c=14$ meters. We want to find the height $b$ on the wall where the ladder touches. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

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

We get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values of $a$ and $c$

Substitute $a = 1$ and $c = 14$ into the formula: $b=\sqrt{14^{2}-1^{2}}=\sqrt{196 - 1}=\sqrt{195}\approx13.9$.

Answer:

13.9