Question

find the length of the third side. if necessary, write in simplest radical form. 4 10

Explanation:

Step1: Aplicar el Teorema de Pitágoras

$$a^{2}+b^{2}=c^{2}$$
Donde \(c = 10\) (hipotenusa) y \(a = 4\) (uno de los catetos). Buscamos \(b\).

Step2: Sustituir valores

$$4^{2}+b^{2}=10^{2}$$
$$16 + b^{2}=100$$

Step3: Resolver para \(b^{2}\)

$$b^{2}=100 - 16$$
$$b^{2}=84$$

Step4: Extraer la raíz cuadrada

$$b=\sqrt{84}$$
Simplificar \(\sqrt{84}=\sqrt{4\times21}=2\sqrt{21}\)

Answer:

\(2\sqrt{21}\)