Question

use the pythagorean theorem to find z. draw 9 12

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are legs, \( c \) is hypotenuse. Here, \( a = 9 \), \( b = 12 \), \( c = z \).

Step2: Substitute values

\( 9^2 + 12^2 = z^2 \)
\( 81 + 144 = z^2 \)
\( 225 = z^2 \)

Step3: Solve for z

Take square root: \( z = \sqrt{225} = 15 \)

Answer:

15