Question

find the length of the missing side. provide an answer accurate to the nearest tenth. 23 inches 20 inches label required

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the missing side be \(a\), \(b = 20\), \(c=23\). Then \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

\(a=\sqrt{23^{2}-20^{2}}=\sqrt{(23 + 20)(23 - 20)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(=\sqrt{43\times3}=\sqrt{129}\).

Step3: Calculate the square root

\(\sqrt{129}\approx11.4\)

Answer:

\(11.4\) inches