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
or

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Here, $a = 9$, $c = 14$, and $b = z$. So, $9^{2}+z^{2}=14^{2}$.

Step2: Simplify the equation

$81+z^{2}=196$.

Step3: Solve for $z^{2}$

$z^{2}=196 - 81$.
$z^{2}=115$.

Step4: Find $z$

$z=\sqrt{115}$.
Using a calculator, $\sqrt{115}\approx10.72$.

Answer:

$z = \sqrt{115} \approx 10.72$