Question

use the pythagorean theorem to find z. draw show your work here hint: to add the square root symbol (√□), type
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Explanation:

Step1: Write the Pythagorean theorem formula

$$a^{2}+b^{2}=c^{2}$$
Here, \(a = 5\), \(c = 13\), and \(b=z\).

Step2: Substitute the values into the formula

$$5^{2}+z^{2}=13^{2}$$
$$25 + z^{2}=169$$

Step3: Solve for \(z^{2}\)

$$z^{2}=169 - 25$$
$$z^{2}=144$$

Step4: Find \(z\)

$$z=\sqrt{144}$$
$$z = 12$$

Answer:

12