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
15
y
16
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 \(a = 15\), \(b = 16\), and \(c=y\).

Step2: Substitute the values into the formula

Substitute \(a = 15\) and \(b = 16\) into \(a^{2}+b^{2}=c^{2}\), we get \(15^{2}+16^{2}=y^{2}\).

Step3: Calculate the squares

\(15^{2}=225\) and \(16^{2}=256\). So \(225 + 256=y^{2}\).

Step4: Add the values

\(225+256 = 481\), so \(y^{2}=481\).

Step5: Solve for \(y\)

Take the square root of both sides. Since \(y>0\) (length of a side of a triangle), \(y=\sqrt{481}\). And \(\sqrt{481}\approx21.93\) (rounded to the hundredths place).

Answer:

$y = \sqrt{481} \approx 21.93$