Question

jaxson is drawing a right triangle with chalk on the outside pavement. the first side of the triangle measures 12 feet, and the second side of the triangle is the longest side, measuring 23 feet. how long is the third side of the triangle, in feet? round your answer to two decimal places.
show your work here
hint: to add the square root symbol (√), type
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Explanation:

Step1: Apply the Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side). Let \(a = 12\) (one leg) and \(c = 23\) (the hypotenuse). We need to find \(b\). Rearranging the formula for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 12\) and \(c = 23\) into the formula: \(b=\sqrt{23^{2}-12^{2}}=\sqrt{529 - 144}=\sqrt{385}\).

Step3: Calculate the square root

\(\sqrt{385}\approx19.62\)

Answer:

\(19.62\)