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 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, \(a = 10\), \(c=17\), and \(b = y\).

Step2: Substitute the values into the formula

$$10^{2}+y^{2}=17^{2}$$
$$100 + y^{2}=289$$

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

Subtract \(100\) from both sides:
$$y^{2}=289 - 100$$
$$y^{2}=189$$

Step4: Find \(y\)

Take the square root of both sides:
$$y=\sqrt{189}$$
Simplify \(\sqrt{189}=\sqrt{9\times21}=3\sqrt{21}\approx13.75\) (rounded to the hundredths place)

Answer:

$13.75$