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
(right triangle with one leg ( x ), one leg 15, hypotenuse 19)
show your work here
hint: to add the square root symbol (( sqrt{square} )), type
oot\
( x = )

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a, b\) are the legs. Here, \(c = 19\), \(b = 15\), \(a = x\). So \(x^2 + 15^2 = 19^2\).

Step2: Solve for \(x^2\)

Subtract \(15^2\) from both sides: \(x^2 = 19^2 - 15^2\). Calculate \(19^2 = 361\), \(15^2 = 225\). Then \(x^2 = 361 - 225 = 136\).

Step3: Solve for \(x\)

Take square root: \(x = \sqrt{136}\). Simplify \(\sqrt{136} = \sqrt{4\times34} = 2\sqrt{34}\approx11.66\) (rounded to hundredths).

Answer:

\(x = 2\sqrt{34}\) or approximately \(11.66\)