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
y =

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 9\), \(b = 10\), and \(c=y\).

Step2: Substitute the values into the formula

Substitute \(a = 9\) and \(b = 10\) into \(a^{2}+b^{2}=c^{2}\), we get \(9^{2}+10^{2}=y^{2}\).

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Step3: Solve for \(y\)

Take the square root of both sides. Since \(y\) represents the length of a side of a triangle (\(y>0\)), \(y=\sqrt{181}\).

$$y=\sqrt{181}\approx13.45$$

Answer:

$y = \sqrt{181} \approx 13.45$