Question

use the pythagorean theorem to find x. 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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x =

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = 11\), \(c=19\), and \(b=x\). So, \(11^{2}+x^{2}=19^{2}\).

Step2: Simplify the equation

\(121+x^{2}=361\). Then, solve for \(x^{2}\): \(x^{2}=361 - 121\).
\(x^{2}=240\).

Step3: Find \(x\)

Take the square root of both sides: \(x=\sqrt{240}\). Simplify \(\sqrt{240}=\sqrt{16\times15}=4\sqrt{15}\approx4\times3.87298\approx15.49\) (since \(\sqrt{15}\approx3.87298\)).

Answer:

\(x = 4\sqrt{15}\approx15.49\)