Question

use the pythagorean theorem to find y. leave your answer as a simplified radical or as a decimal rounded to the hundredths place.
draw
12
15

Explanation:

Step1: Write the Pythagorean theorem formula

$$a^{2}+b^{2}=c^{2}$$
Let \(a = 12\), \(b = 15\), and \(c=y\).

Step2: Substitute values into the formula

$$12^{2}+15^{2}=y^{2}$$

Step3: Calculate the squares

$$144 + 225=y^{2}$$
$$369=y^{2}$$

Step4: Solve for \(y\)

$$y=\sqrt{369}$$
Simplify \(\sqrt{369}=\sqrt{9\times41}=3\sqrt{41}\).
As a decimal, \(\sqrt{41}\approx6.403\), so \(y = 3\times6.403\approx19.21\).

Answer:

$y = 3\sqrt{41} \approx 19.21$