Question

use the pythagorean theorem to find z.

Explanation:

Step1: Write the Pythagorean theorem formula

$$a^{2}+b^{2}=c^{2}$$
Here, \(a = 5\), \(b = 12\), and \(c=z\).

Step2: Substitute the values into the formula

$$5^{2}+12^{2}=z^{2}$$
Calculate \(5^{2}=25\) and \(12^{2}=144\). Then \(25 + 144=z^{2}\), so \(z^{2}=169\).

Step3: Solve for \(z\)

Take the square root of both sides: \(z=\sqrt{169}\). Since \(z>0\) (length), \(z = 13\).

Answer:

13