Question

use the pythagorean theorem to find z. leave your answer as a simplified radical or as a decimal rounded to the hundredths place.
draw
show your work here
hint: to add the square root symbol (√□), type root
z =

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b = 13\), and \(c=z\).
So, \(12^{2}+13^{2}=z^{2}\).

Step2: Calculate squares

\(12^{2}=144\) and \(13^{2}=169\).
Then \(144 + 169=z^{2}\), which is \(z^{2}=313\).

Step3: Solve for \(z\)

Take the square root of both sides: \(z=\sqrt{313}\).
Calculating \(\sqrt{313}\approx17.69\) (rounded to the hundredths place).

Answer:

\(z\approx17.69\)