Question

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

Explanation:

Step1: Identify the right - angled triangle

The ladder, the wall, and the ground form a right - angled triangle. The length of the ladder is the hypotenuse ($c = 15$ m), and the distance from the base of the ladder to the wall is one of the legs ($a = 9$ m). We want to find the other leg ($b$), which is the height on the wall where the ladder touches.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $c = 15$ and $a = 9$ into the formula: $b=\sqrt{15^{2}-9^{2}}=\sqrt{(15 + 9)(15 - 9)}=\sqrt{24\times6}=\sqrt{144}=12$.

Answer:

12