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: Recall the Pythagorean theorem

\( a^{2}+b^{2}=c^{2} \), where \( c \) is the hypotenuse. Here \( a = 5 \), \( c = 10 \), and \( b=y \).

Step2: Substitute values into the formula

\( 5^{2}+y^{2}=10^{2} \)
\( 25 + y^{2}=100 \)

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

\( y^{2}=100 - 25 \)
\( y^{2}=75 \)

Step4: Find \( y \)

\( y=\sqrt{75} \)
Simplify \( \sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\approx5\times1.732 = 8.66 \) (rounded to the hundredths place)

Answer:

\( y = \sqrt{75} \approx 8.66 \)